Try turning the phone to landscape mode before tapping the full screen button. It works for me in YouTube on Pixel 7a.

I turned off auto-rotate, so when I rotate the phone I get a symbol in the top right corner to notify me that the screen rotation is locked and I just press that and the screen rotates to the current position. I use a Galaxy Fold 5.

This may not be helpful to you in particular, but I wanted to throw this out there.

I don’t like Auto Rotate because apps can undesirably rotate when the phone is in odd positions. However, I think it’s great for video apps, camera apps, and photo galleries.

Auto Auto-Rotate fixes this. It’s free and open source. When you toggle the Auto Rotate setting on or off, you’re doing it for just the current app!

So now I just rotate my phone the way I want and YouTube matches. No need to hit the full screen button.

Also, if you don’t know, in the YouTube app you can swipe a video up to make it full screen without having to use the full screen button. Of course, it’ll rotate the “natural” way first, which is what’s annoying you. Just thought I’d mention it. I sometimes use that feature when my phone is flat on a table while I’m eating or something and I don’t want to pick it up to engage auto-rotate.

To work best, Auto Auto-Rotate equires a persistent notification, but even with that off, it will work for a long time before you have to relaunch the app. Battery optimization for the app should be off, of course.