Yeah, the issue is they have a Linux game client, but they don't have a Linux version of their launcher... so you have to use Wine/Proton/some kind of compatibility layer (and you have to do some work to get the files you need to make that happen), but it's even more convoluted than that. Just to give you an idea... https://www.reddit.com/r/2007scape/comments/11q8mly/how_to_run_jagex_launcher_on_steam_decklinux/
I'm shocked it took them this long to implement it. I hope eventually you could have multiple characters on one account. I would like to play an iron man but don't want to pay for a second subscription.
It's a nice feature. Also, when the jagex acct servers go down again like they have somewhat recently, you can still open runelite like normal to sign in.