I have MacBook Pro M1 Max, with two monitors, one 34" as the main monitor and one 24" as the side monitor which I use vertically, after upgrading to macOS Ventura this issue started to appear! When I tried to watch a video on my main monitor when I switched to full screen, it was showing it sideways!
I'm a software developer so I have multiple browsers, I tried on all of them, and sometimes one was rotating but not the other, but after some time, all were rotating!
I tested Youtube, Amazon Prime, HBO on browsers, and then even the Apple TV app, they all show the videos sideways in fullscreen mode!
But it was happening only on the main monitor, not the side one, not the laptop's internal screen!
Interestingly, the image was showing normal if you moved the mouse pointer on that screen, but as soon as you stopped the mouse, the video go back to the rotated state!
One thing I found out about this was that if you restart the OS, the issue goes away, but after a few times of Sleep/Awake circles, sometimes same day but definitely the next day, it'd come back, and I have to restart the laptop again and again!