Up until yesterday, I have been using safari on my iPad Pro to AirPlay movies. I used Airplay, from the second page of the control panel, not AirPlay Mirroring from the first page. Audio and Video were rendered perfect;y.
From yesterday, the video doesn't show on the TV, only on the iPad. However the audio streams to the Apple TV 4 perfectly.
I have tried rebooting everything. I'm suspecting an IOS or TVOS update has caused this, as it changed from one evening to the next with no settings changes done by me at all.
it sounds very similar to the OP. I think it may be linked, and if so, it is likely to be TVOS that is causing this.
Edit: AirPlay mirroring (page 1 of control panel on ipad) still works, even though AirPlay (page 2) is broken. The problem with mirroring is that the video is not full screen. It has a wide black border, and the resolution is not nearly as good as it was when I was using Airplay.