Content and Privacy Restrictions on macOS 27.0.1 should function normally and as on past versions of macOS.
See the following from Apple: Change App Store, Media, Web & Games settings in Screen Time on Mac - Apple Support
More general information here: Change Content & Privacy settings in Screen Time on Mac - Apple Support
If content restrictions continue to fail in Safari, use System Settings > Screen Time > App Limits to add Safari or set a strict 1-minute daily limit on web browsers and focus-hindering sites as a temporary workaround.
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
If the issue occurs in safe mode and in a new user account, that makes it likely to be a bug in macOS 27.0.1. Bugs should be reported to Apple here:
Feedback - macOS - Apple
