Have you tried moonlight? An alternative to steam link. You can use install it on the lg tv by sideloading the app.

Alternatively, you can plug in a Raspberry Pi that runs steam link :)

Oh yeah I’m aware of various “plug in a thing” options, just thinking it wild be nice to have to, particularly if a single controller paired to the TV itself could operate the outer shell as well as Xbox and steam streaming.

My LG C2 hardware isn't powerful enough to stream higher than 60hz at 1080p, if I remember correctly. It also needs a LAN cord for consistency since the tv wifi adapter is not good. Instead I put moonlight on my steam deck and plugged that into the tv.