I think the HDMI stick that has a older A chip and less RAM that is purely for video/music streaming etc is becoming a good idea as the RAM prices shoot up and may hit the $/£99 price point, especially if it uses the A16 chip.
A "home hub" version that adds a thread border router and chip/RAM powerful enough for Apple Intelligence with perhaps an A18 chip could come in at $/£149 .
I simply can't see a gaming version launching though... Apple would need to convince the studios to port their MacOS versions to TvOS (and even if this is simple, it still requires resource) and it would likely need 512 GB minimum given how large games are getting (the new Crimson Desert game
needs 150 GB), and Apple would likely have to sell it with an Apple-branded controller. At this point, this is basically a Mac Mini. A much better approach would be to develop a "big picture mode" for MacOS that would let a Mac have a controller/media based interface that could be automatically launched on boot that mimics TvOS. Then, anyone that wanted a gaming Apple TV could just use a Mac Mini with their choice of controller.