There have been many issues reported with Mission Control and Spaces on macOS 27 Golden Gate, including with the Assign to Desktop function and especially regarding the way Full Screen apps and app switching are handled. Some have been resolved by identifying and removing incompatible 3rd party extensions, others are bona fide bugs. The minor point update, macOS 27.0.1, did not appear to address the more significant issues.
Bugs should be reported to Apple here:
Feedback - macOS - Apple
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.
It might help to download and run EtreCheck, written by a long-time forum member. The free version is fine. Post the full report using the Additional Text button. No personal information is revealed.
If the issue persists in safe mode and a new user account, that suggests that it's a bug that Apple needs to address.
Reporting issues like this to Apple is the only way to get them fixed. They do prioritize bugs based on frequency of reports, so the more people who report it, the faster it will be addressed.
Personally, Mission Control is working fine for my use cases on my 16" M4 Pro MBP running 27.0.1. I have many Spaces and open windows, but I don't use assign to desktop or full screen apps and I don't have my apps grouped, all of which are associated with reported issues.
