I've found that adding or ticking the check for LogMeIn in Accessibility and most importantly, in Screen Recording (after Catalina) worked. You don't mention LogMeIn.app. I have that in my list and that is checked on.
I have AEServer in my Accessibility and that is NOT checked on. What exactly does that do?
Being that there are several items in System Preferences that need to be checked, maybe it's best that we get a definitve list. And better would be that LogMeIn does all the check boxes or walks us through all of them like it does for SOME of the settings.
Here are all the possible ones I can find:
Microphone
LogMeIn.app
Accessbility
AEServer
LMIGUIAgent.app
LogMeIn Client
LogMeIn.app
Full Disk Access
LogMeIn Control Panel
LogMeIn.app
Files and Folders
LogMeIn Client
Downloads Folder
Documents Folder
Desktop Folder
Screen Recording
LogMeIn.app
I'm working fine with the way mine are set now, but not all of them are checked on so it would be nice to know what all of them do and which are needed on, since I don't have AEServer on and I'm working fine for what I need to do.