This issue has been reported by users who have installed 3rd party tools, for example Raycast (even though it appears unrelated, extensions run at a low level and incompatibilities with macOS updates show up in unexpected ways).
https://github.com/raycast/extensions/issues/32519
The issue is not with macOS, but rather with the incompatible extension(s). 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. If you want to use such utilities, contact the developer(s) for updates or to report issues.
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.

Personally, I do not have any such extensions installed, and I cannot replicate the issue that you report on my 16" M4 Pro MBP running 27.2. The 'pipette tool' (aka eyedropper / color picker) works fine in native apps like Pages and in 3rd party apps like Photoshop CC.
