Basic descriptions are necessary for collaborative storytelling

My main problem comes from people with charisma: 8 on their sheet trying to "just talk it out" and succeeding on the strength of their real life personality. I know you're personable in real life Alex but you dumped charisma now sit down and let someone else have a go.
When playing a face I usually sound like "I flash my most disarming smile and, fully sincerely, tell him if he surrenders no harm will come to him." Third person narration. I don't usually want to go line by line.

Totally depends on the vibe. In my group, acting out persuasion or deception checks is most common, but sometimes someone can't think of exactly what to say and so just outlines the gist in a detached way - e.g. "I go on about how the safety of the city is top priority, allow us access so we can continue our search for the fugitive". Not specific, but general. Either works, and the general form is bare minimum IMO.

Players Decide, PCs act.
You tell me what your PC wants to achieve and how. I set the DC to check how well they perform at that attempt (or declare "no roll needed", because it's trivial / impossible).
You want to persuade an NPC? Tell me the gist of your argument and I'll consider how receptive your target is and set a DC for checking how well your PC can present said argument.
(In some cases like "I want to hit them real good with my sword" or "I want to climb up that wall", no detailed description is necessary, we both know what you mean.)

I struggle with this, I make a minor effort but what am I meant to do when my high Cha, high Diplomacy character is more charismatic and diplomatic than me? :( I either skimp on the RP or do some very unrealistic RP as my awful unconvincing wording magically convinces the NPC anyway.
- Third-person narration is the key. IRL I'm the harassment guy from the "flirting vs harassment" meme but I can still describe how I want the interaction to go even if I don't know the words that would make it go that way. Something like "I smile with absolute confidence and talk to him as if he couldn't possibly disagree that I was his new best friend. And he would never let a friend down when all he had to do was let me in without checking all the boring paperwork!"

The barbarian isn't going to just say "I roll athletics" without explaining what they are trying to achieve. Same for persuasion. "I try to convince the mayor we are experienced enough adventurers to assist" is enough to let the GM know what the intention is and give context for the NPC's possible reponse.
- A player playing a barbarian isn't expected to deadlift a boulder IRL to prove his character in game is strong.
  Why should a player playing a warlock be required to make a persuasive argument IRL to get to prove his character in game is persuasive.
  I mean I get a little narration makes the game more fun and diving into the social aspects are just as important as the combat. But We are playing a fantasy game to let people embody whatever fantasy they want and some people just might want to be a lot more charismatic
  
  I feel like you've missed the point of the comment you're replying to
  No, a barbarian is not expected to deadlift IRL. But if a barbarian walked into the middle of a situation and declared he was going to solve it with Athletics, without explaining how he was going to do that, he would be met with blank stares. You need to state intent. "I'll use Athletics" is meaningless. "I'll pile up these boulders into a staircase so we can climb over the wall" is a course of action.
  Similarly, "I'll use Persuasion" is meaningless. Worse, are the people who just say "I've got proficiency in all the charisma skills, so I'll just use whatever one's most effective" lol. "I'll use my wit and charm to convince the guard that we have been invited to the castle" is a course of action. "I'll use facts and logic to convince the guard that it is in his best interest to allow us into the castle" is a course of action. I don't care if you're charismatic in real life, but if you can't even summarize what you're trying to say, how is the rest of the game world supposed to respond to it? "I'll Persuade them" is only the first half of a sentence.

If Brayden says his character tries to lift a heavy rock and he proceeds to deadlift 150kg to demonstrate, heck, I'll give him inspiration.

A character performing a persuasion check should attempt to describe and act out their persuasion.
Once complete, the GM should evaluate the description, and use that as a modifier to the persuasion roll.
A character that says "ummm, IDK, I guess I just try to influence them using my high charisma" should get no modifiers to the roll. A character who tries but entirely flubs the conversation should get a -1 (when appropriate), a great performance with an entertaining flourish to the description should get at least a couple ++ to the roll.
- Yes, but if you don’t offer the same accommodations for the person who goes into excruciating detail about how they lift up an iron grate, there’s a bit of an unfair imbalance there. Same goes for someone who can’t necessarily verbalize an entire conversation on the subject, but can say, “I’d like to try and persuade the Governor that we’re perfectly capable individuals, and specifically bring up how we took care of the rats in the tavern cellar, as well as how we turned away the bandits attempting to burgle Mrs. Henderson’s store.”
  If you don’t allow for either of those types of situations, you’re just promoting people who have a real-life charisma over those that don’t.
  
  But you would do that. Someone that just says "I force the iron gate open with strength" gets no bonus, just a straight roll. Someone that says "I look for a weak spot in the gate and use a pry bar that I found earlier to force that spot open" maybe gets a +2 to their roll for extra thinking.
  Also, it depends on the group, you don't need a one size fits all for this. If you have one or two people who are uncomfortable with going into detail, then you have to adjust your GMing to match the situation. But if there's just someone who needs a little encouragement, then you start throwing bonuses for extra roleplaying left and right.
  The whole point is to make it fun for everyone (including the GM) so you're going to give bennies for out of the box thinking and extra effort, appropriately scaled to the group you are in.
- Someone after my own heart. Say what you’re going to say and I’ll decide the DC. Just say “please” and probably get a straight check DC 12-14. Insult the guard’s mother and children will likely get a DC of at least 15 and maybe disadvantage. Going above and beyond probably doesn’t require a roll and nets you inspiration.
  
  Do the same thing with combat. A barbarian that says "hit with axe" every round just gets a regular chance to hit. A barbarian that says "I charge in yelling my battle cry swinging my great axe while kicking over the chair between us as I advance" might get a +2 to attack that round (as long as they don't use the same thing every time.)

I had a game in Middle School that involved describing how I was supposed to arrange a ladder to climb up the side of a wall. We went back and forth for over an hour, because my DM kept insisting I couldn't turn the ladder sideways.
Now, if my players want to deliver a particularly clever bit of prose or describe a novel engineering technique, I just give them a +2 on the roll and that's that.

In my games the DM calls for a check. The player describes their intentions and then the DM calls for a check when appropriate. So if someone gives really good reasoning for an NPC to act a certain way, there might not be a persuasion roll, if the character says something dumb then the roll DC might increase. The point is, no one is allowed to say “i roll persuasion to get them to do X”
- Mhm. You don't have to be particularly eloquent for it, but a basic description of what your character is trying to say goes a long way. "I persuade the guard to let us past" won't get you much, but "I appeal to the guards better nature, and use our shared occupation/love of X/ my most attractive smolder to ask the guard to let us past" will do great things in either the DC or getting advantage.
  
  Yeah. I like giving advantage/disadvantage because it tells the player: your roleplay positively/negatively impacted the outcome. Luckily i am blessed with good players that will play their characters even if it means a less than ideal outcome.

Sentences like "Can I roll for persuasion?" or worse "I perception the room" are one of my biggest pet peeves coming from players. Tell me what you want to accomplish, I will tell you whether and what you need to roll. I've mostly managed to train that behavior out of my players, thankfully. As a newbie DM I used to use die rolls as a crutch -- "this is a dice rolling game, so the more dice we roll the more fun we're having, right?" I thought. I also hated saying no to my players, so stupidly high DCs were a way to shift the blame onto the dice for my players' failures. As I've gained experience, I run a much less dice-heavy game. I very often just let my PCs succeed with no roll required.
The one case where I don't mind the players asking to roll is when they ask to "INSIGHT CHECK" à la critical role; it's always fun to see the players so passionately engaging with NPCs.
- My complaint is when I have a PC with an insane charisma score and the DM wants me act out the conversation, then I fail in my persuasion without rolling. “The NPC would not be convinced by that”
  Maybe I am not being very charismatic, but my PC is! Let me roll for it! You don’t make a mage fail in their spells because they can’t do magic in real life, do you?
  
  The way I see it, there's nothing wrong with voicing your opinion, especially between games. Saying "hey, I feel like the fantasy of my character isn't coming to life, is there any way I could get you to take the Charisma score of my character in greater consideration during social interactions going forward?" after a game is a great way to deal with that. That said, there's only so much that Charisma can account for. No matter how charismatic you are, you won't persuade a king to give up his kingdom. Your DM likely thinks your arguments are just too weak for you to persuade someone, regardless of your Charisma. Maybe their expectations regarding your wit and roleplay are too high, or maybe you need to re-evaluate your expectations of what is possible in your game.

I dunno, i appreciate being able to gloss over certain mundane actions with the shared understandings of common actions. Shopping, for instance, takes loads more time when everyone's in storyteller mode, and you never really know how many more sessions you've got before a scheduling error comes up. Best to keep the routine parts brief.
Schmoozing a merchant for a better deal is best handled with a persuasion check, assuming getting a good deal isnt an important part of the campaign.

In my opinion if the player doesn't tell me their Intent, what they are trying to achieve, how can I assess difficulty? Assess danger? Imagine consequences? I also want the tools for the task they set themselves upon. For the barbarian weapons used, positioning etc. For the talker their arguments. Acting out is not necessary.
Or just use an apocalyptic principle: "to do it, do it". If the character doesn't do anything that triggers a move no move is triggered.

Basic descriptions aren't necessary but helping in a lot of cases. And in some it's completely the same ("I want to roll an insight check" vs. "Do I believe his story?" - there's simply no describeable process making a difference).
Also players are different... I won't punish a guy playing a high int, high charisma character for not coming up with a logical or persuasive argument (and again "I want to talk to him to change his mind" vs. "I want to roll for persuasion" is all the same here), just as I don't punish a nerd playing a barbarian for not actually being able to lift a person one-armed.
But then I know my players and assume new additions are acting in good faith to their best ability and not just roll-playing because they want to have more time to focus on Candy Crush.

Now I want to play a one shot of extreme DND where every skill check has a real life equivalent. Making a DC 25 knowledge check? The answer is in one of these books, you have 15 seconds to look through them.