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You can go into Shortcuts and set up an Automation to automatically lock/unlock orientation when you open/close any app (including this one).

Oh that's really nice, there are certain apps where this is very useful and I would prefer it but definitely it's off for me globally.

This doesn't totally solve the issue, but if you unlock your phone's orientation, rotate to landscape, then go to settings, you'll find a "lock current orientation" setting.

If your video demands are not complex, this app should work for you:

https://apps.apple.com/nl/app/horizon-camera/id778576249