I have a 4k projector running Android 9, however, the OS resolution is 1920x1280. If I play a movie in an app running on the projector is it possible to get 4k resolution?
I tested this a lot. Using the Jellyfin app (it's like Plex) running on the projector itself, 4k movies look as good or better than playing from a PC that is 4k connected via HDMI.
Every 4K video you play will be downscaled to the resolution your device supports, that's all.
One way to check: does your projector have some kind of OSD where it says what kind of signal it's getting?
There are "4K Test Patterns" clips on YouTube or you could probably find the same clips on the interwebs for download if you want to add to your Jellyfish NFS. Some of the test-patterns will have a box/square made up of horizontal lines that if viewed at full 4K you will see the gaps/space between the lines, but if the same clip is only rendered at 1080p those same lines bleed together and there is no definite line separation.
It is normal for AndroidTV to render the UI at 1080p, and actual 4K media will be correctly rendered at 4K if the display/TV/projector supports 4K.
Android tv runs ui on fhd if 4k but content is full resolution