I plugged my Roku stick into my projector HDMI port, and it seems to work fine, except when I add a channel it does not show up on the home menu's icon channels.
I have played with the settings, where there is a display short cuts, which doesn't seem to do anything.
The projector is a Jafar, and it worked on older Roku sticks. It does auto-sync for 1024 or .7. I tried locking different screen resolutions on the projector, but no change.
To make it work, I search the already installed channel history, reselect the app icon installed, and start a channel that way.
This is a Roku streaming stick 4K media on a projector 1K.
I've seen a few people report something similar, but I don't think I've seen a definitive solution. Make sure you perform a "System restart" from Settings->System or Settings->System->Power (as appropriate) to see if they show up. You might also want to check for a "Software update" from Settings->System while you're at it.
So my updates were current, so that wasn't the issue. I restarted from cold power off, to try the system reset but it started working. Not sure of anything but a power off/on.