Can you explain what the point of Bazzite is? I don't really understand what it adds over installing Lutris onto whatever distro you would otherwise have used

You can indeed install everything manually (it won't be just lutris though, there are many possible tweaks).

SteamOS/Bazzite/uBlue project are Linux distros with immutable core. The immutable part is tweaked, tested, fixed in time and can be easily switched/rolled back. Many people (me included) find it much nicer experience to get some battery included base that someone more competent put together and that can't be easily broken. So instead of figuring out how to put linux parts together you find immutable distro that fits most of what you need and then install just what is missing.

It’s just an opinionated, gaming-centric build of Fedora Silverblue/Kinoite. It ships with everything preconfigured for typical gamers that just want a low barrier to entry and low maintenance burden. It’s extremely plug-and-play.

I like my steam deck and got tired of waiting for the steam machine. I asked one of the AIs for something similar and it told me to install Bazzite. Took me an hour and I got the Steam-like UI that I wanted. I did not explore other options because my problem was solved.