Never heard of the tool, but by the sound of it, it extends your battery life by letting you not charge to 100% (e.g. only charge to 80%).
That's real. Doing that will prolong the life of your battery.
Should you pay $25 for a tool that will do that? Well, if you're on Android 12 (edit: and your device manufacturer has implemented it), there may be an option in the battery settings to limit charging to 85% which gives you most of the benefit.
If you're not on Android 12 but have a rooted phone, you can get a free app that does the same thing.
If protecting the battery is important to you, you don't have a rooted phone (and don't want to root it), and don't have Android 12, then as far as I can tell from reviews, Chargie does do what it says.
To be honest I don't know why. Manufacturers from Samsung to Apple to Microsoft say is the case, but I haven't managed to find an answer with a better source than itself.
I get the impression that it's about staying at high levels of charge.
So when I go to bed I put my phone on the charger. After about 1.5 hours it is at 100%, then it spends the rest of the night on the charger at 100%. It spends 1/4of its life on the charger at 100%. From what I read of this, if it was taken off the charger and allowed to discharge, it would be less of an issue than having it at 100% then every time it drops to 99% the charger tops it up to 100% again.
But TBH I have not found anything that backs up the idea of charging to 80% only vs charge to 100% and taking it off the charger (you can get apps that give you a notification when it gets to a certain charge level). Lot's of people and articles talking about it as a known fact, but not so much in the way of sources.
Sorry, I read this during an internet search but it turns out it's not in AOSP but something that various device manufacturers have implemented.
While searching I found GrapheneOS say they will not add this feature as it's not privacy related, and that the OS is not rootable, so you might be a good use case for Chargie.
I didn't save the source but I believe is was just someone talking about some mainstream phone, assuming it was baked into android. The downfall of using internet comments for sources.