I recommend bodhi linux. I was looking for something similar to arch and i think this is a good alternative. I have been using it for about 3 years now and had no serious issues. They recently updated to 7.0 and now the packages are much more up to date.

It is based on ubuntu 22.04 and uses apt as a package manager. I find installing nix package manager alongside it can help get any packages it doesnt have, but i havent really had much issue with that since moving to 7.0

Its designed to run on old hardware, and i can vouch it works fine on a system with 2gb ram so it will not use much resources.

It comes with thunar as manager and terminology as terminal. I have also used pcmanfm and mate terminal on the system and they work fine as well.

It uses moksha desktop environment which is a fork of enlightenment but i have also used lxde on it as well and switching was not hard.

I dont really game on it since it is on low end hardware but it should have no problem with retroarch on a more powerful system.

It has synaptic package manager for gui installs but tbh i haven't really used it since i use cli for that. You shouldn't have any trouble installing flatpak on it as well. And you should be able to use obs on it (tho i haven't tried)

I would say this distro should do most of what you want extremely lightweight and mostly out of the way (don't really get notifications on it).

It requires a bit of tinkering at first because it is minimalist and only ships with the minimum required packages but this gives the option to put the packages only you want on there. But once you're set up you really won't have to change anything