I almost exclusively use desktop mode. One of the main reasons I got a steam deck was to have a Linux PC connected to my TV at all times. I watch a lot of sports via pirated streams, and those only really work well in a web browser. A raspberry pi 4 was not quick enough to keep up with it, but the steam deck is more than capable.
Currently, just when I have to use it to install anything that I can't install via game mode, and when I need to tweak the system or game files, copy roms from my NAS, etc.
I mostly use it to set up Non-Steam Games like Diablo. Once set up, I go back to gaming mode. I once briefly considered using it to resolve a server issue for a business client (by using SSH which for who knows why is expensive as fuck on iPad), but decided against it -- I was home to relax not work.
When I first got my Deck I installed several emulators for nostalgia (of course for games I own legitimate versions of), but after recently re-imaging my Deck I haven't had the urge to do that again. I got what I needed, and may do it again some day; but for now I'm satisfied by Steam games and Diablo.
I use a Arch Linux install (configured to have a 'as close as possible to SteamOS 3' experience, so I still have the usual gaming mode and desktop mode) and I use desktop mode for web browsing, programming (and related stuff), system maintenance and installing stuff.
I'm in the same situation, the Deck has been my only PC for about as long as I've owned it (first batch, so about a year and a half now) and it's more than enough for my use case.
There was a period of time where I was too lazy to re-hook up my main PC to everything. I just hooked up my Steam Deck instead via a USB C hub.
It was then that I realized I don't really use my main gaming PC anymore. I just play on the Steam Deck and almost everything else is just general use most of the time.
Since then, I found I still prefer to do some tinkering on a way the Steam Deck isn't very good at, so I been thinking of selling off my PC and buying a capable laptop to have that extra ease as I found I don't need the extra performance anymore.
I have been using mine to read comics recently, since the screen is larger than my phone's and the aspect ratio is about right when turned on it's side.
There are some movies/websites that don't work well with Chromecast. Being able to play them on my steam deck while docked is often the easiest way to play them.