You can't really avoid a long running process for a game launcher though. It's just how they work, you need to keep track of play time and respond to any API calls from the game. But it could be a native background daemon instead of two Steam Web Helpers.
I disagree. I get that steam has useful features I want while in-game (e.g. invite a friend to play), but there's no reason it couldn't just run this launcher only when a steam game is running and immediately exit once it's done.
Also, I think a lot of people forget how small well written software can be -- we're talking like single or double digit megabytes. Heck there's a whole linux distro that's under 20mb.
The only benefits of Tauri are the smaller application package and the fact that the runtime is always up to date (which can also be a downside). That full package doesn't live in RAM when it's running, so it's "merely" wasted disk space and not RAM. In terms of RAM it uses just as much as electron or CEF.