After connecting Apple TV 4K to projector, it doesn't work on any other TV.

I have an Apple TV 4K that is usually hooked up to a 4K TV. I moved it temporarily to an old projector I have and connected it via an HDMI to DVI adapter.

It worked great, but when I put it back on the original TV, it turns the TV on, but I get "no signal" messages from my TV. After trying multiple TVs, cables, etc., I connected it back to the projector and it worked fine there again.

It seems that the Apple TV is stuck in 1024x768 SDR resolution and won't autodetect any other resolution. I tried to reset the Apple TV while connected to the projector, but it still picks up the 1024x768 resolution. I figured that I should be able to unplug it before the final boot, but I'm worried that I might brick it if I unplug at the wrong moment.

I also tried to reset the resolution while connected to the 4K TV by memorizing the menus (since there is no display), but it is not easy to control the menus blindly (e.g. three down, ok, two down , ok, one ip, ok) with Siri remote touch pad and I never seem to be successful.