Take my money!

https://hometheaterreview.com/optoma-uhd55-new-3600-lumen-gaming-and-movie-projector/

This new projector relies on pixel shift technology to achieve 4K resolution. Because this projector is equipped with HDMI 2.0, and not HDMI 2.1, it is not able to handle 4K refresh rates beyond 60 Hz. However, it is able to provide up to 240 Hz refresh with 1080p content, and it advertises a very gamer-friendly input lag of only 4ms for 1080p at 240 Hz, and 19ms at 60Hz and 4K.

I would be worried about power consumption @3600 lumens if also using as a large TV, with the huge bump in recent electricity prices and worse coming. It can only provide 95% DCI/P3 coverage at reduced brightness levels. Its not really 4K at 60Hz due to the pixel shift. Though lamp life isnt bad at 4 to 10,000 hrs, it depends on the replacement cost. It does 3D, that might make it worthwhile, if only gaming support hadnt quit the technology.

TronicsFix recently repaired a bunch of Optoma projectors. The flaws were quite strange, like loose internal connectors and screws. I don't know how good and respected, generally speaking, Optoma is, but that was a pretty weird repair video.