I’m on the same boat, I’m not interested in phone gaming especially due to having to use a touch screen but a few months ago I got myself an Android stream box, one of the best decisions I ever did, not only do I use it to stream youtube, netflix, disney and such but I also installed several emulators from Playstation to Dreamcast to N64 to PSP to Saturn and honestly I have been using it for gaming more so than most of my actual gaming devices in the past few months, my Playstation is collecting dust as I’m using its controller with my Android stream box.
It’s exactly how you described it, pick up and play, watching youtube or netflix? Just switch the app, activate controller, play games. ironically I initially bought it to be able to stream my PS Vita on TV, unfortunately that didn’t work because this feature is no longer supported since Android 10 which my Android device is running on, but I mean I can use it to play PS1 and PSP so 2/3 ain’t bad and I get Dreamcas and N64 as well so I wouldn’t call it a loss.