“Your screen is being observed” Mac Message

The OS or any apps written by Apple included with it will not produce such errors. Such as, a simple full screen shot keyboard command of Command+Shift+3 will produce no error even though it is obviously accessing the screen. The luxury of being able to declare yourself safe.

This means you need to find out what third party software you've installed is causing the message to appear.

Are you seeing this as soon as you turn your Mac on, or when you're trying to use a specific app? If the former, it may be the drivers for a Wacom, or other brand of tablet. As an example, the Wacom drivers in Big Sur have just the one entry that needs to be declared "safe" by you in System Preferences > Security & Privacy under the Privacy tab. There are more of them for Wacom in Catalina.

Another way to check is to see what startup daemons have been added by third party software you've installed. These entries exist as one method to cause an app to load as the Mac starts up. Entries in the .plist files point to the app, or sub-app buried within an app. Whichever they are, the OS acts on and loads them at startup.

There are three locations. If you double click the main drive icon on your desktop, the first two are in the Library folder next to Applications, System and Users.

/Library/LaunchAgents

/Library/LaunchDaemons

The last is in your user account. The tilde ~ means your account. Not the main Library folder.

~/Library/LaunchAgents

I have these in Catalina:

/Library/LaunchAgents

com.adobe.AdobeCreativeCloud.plist

com.adobe.ARMDCHelper.cc24aef4a1b90ed56a725c38014c95072f92651fb65e1bf9c8e43c37a23d420d.plist

com.adobe.ccxprocess.plist

com.adobe.GC.AGM.plist

com.adobe.GC.Invoker-1.0.plist

com.microsoft.update.agent.plist

com.wacom.DataStoreMgr.plist

com.wacom.IOManager.plist

com.wacom.wacomtablet.plist

com.xrite.device.softwareupdate.plist

com.xrite.i1Profiler.tray.plist

/Library/LaunchDaemons

com.adobe.acc.installer.v2.plist

com.adobe.agsservice.plist

com.adobe.ARMDC.Communicator.plist

com.adobe.ARMDC.SMJobBlessHelper.plist

com.aladdin.aksusbd.plist

com.aladdin.hasplmd.plist

com.bombich.ccchelper.plist

com.charlessoft.pacifist.helper.plist

com.empiatech.cmio.DPA.plist

com.github.IngmarStein.Monolingual.Helper.plist

com.microsoft.autoupdate.helper.plist

com.microsoft.office.licensingV2.helper.plist

com.prosofteng.DRInstaller.plist

com.quark.quarkupdate.quhelper.plist

com.quark.QXPHelper.plist

com.twocanoes.WincloneHelper.plist

com.wacom.displayhelper.plist

com.wacom.UpdateHelper.plist

com.xrite.device.xrdd.plist

com.xrite.device.xrdd.restart.plist

~/Library/LaunchAgents

com.adobe.GC.Invoker-1.0.plist

com.linotype.FontFolderProtector.plist

As you can see, there can be quite a few. The only ones I have that would have anything to do with screen access would be for the Wacom tablet. The rest launch services and helpers that need to be active for each third party app listed to run when launched. A lot of them are just services that check in the background for updates for each respective app.

Since we can't see your system, this is decent info to give you an idea where to start looking.