I cannot replicate the issue that you describe. I am running macOS 27 Golden Gate on an M4 Pro MBP, in this case connected to a 5K:2K external display. I have the Menu Bar set to hide in full screen only:

I opened the Apple WWDC 2026 Keynote in YouTube (Safari), clicked the full screen button, and as you can see from the screenshot...no menu bar.

Similarly, I opened a family vacation video in QuickTime Player and in VLC, clicked the green stoplight for full screen, and in both cases, no menu bar (unless I move the cursor to the top, in which case it appears).

Accordingly, this does not seem to be a general issue with macOS 27 Golden Gate.
Have you rebooted your Mac? If not, that's the first step. If that does not help, then see if the problem is present when you boot in safe mode. That process performs some system cleanup and clears caches, and also disables 3rd party extensions that may cause problems.
Start up your Mac in safe mode - Apple Support
If that does not correct the issue, test in a new user account. A newly-created user account will have all settings at default, and if the issue does not occur in that new account then it provides guidance on what may need to be changed to correct the issue.
Add a user or group on Mac - Apple Support
Once the testing is complete, the new account can easily be deleted.
Delete a user or group on Mac – Apple Support
Those steps will help to isolate the problem.
There may be something about your system that is causing this, and it may be a bug affecting only some models. Bugs can be reported to Apple here:
Feedback - macOS - Apple