So - I have a steam deck. It doesn't care about how big your tv is, but it's not gping to drive 4k performantly. I play diablo 4 on mine at 1280x1024 (i think - i should double check) and it's very playable. For older games at native resolution its dreamy. Yes bluetooth peripherals work.
If you want, pick a day and time and i'll come over and let you try it out - plug it into your big monitor and play some games. If theres a demo i'll even pre-install stuff, or you can try my games. (Can you log in on the deck without blowing up my stuff? I dunno.)
You'd be surprised. Go look on youtube, plenty of people demoing those at various resolutions on the steam deck. It's surprisingly powerful. I think you are putting too much emphasis on 4k - none of the 32-bit stuff you cant run on the mac will be 4k anyway.
@Biggles good point - but I ran at 4K resolution where possible the last 7 years (downgraded to 1080p sometimes though)
For gaming? I mean, for desktop text and such it makes sense, or obviously 4k video - but resolution past a certain point is kinda lost, especially with FSAA and other similar tech; versus things like higher frame rates.
But I am like Sam I Am: "Try it! try it! then you'll see!"
I bought my steam deck sight unseen, no demo, a solid year before I got it. You don't need to do that.
@Biggles given the hardware requirements to run e.g. Doom Eternal or Borderlands 3 at a good frame rate, it was probably wishful thinking on my part that a Steam deck would power that at 4K resolution =\