For clarification: the working version, 11.5.5, was an upgrade from a prior version of 11.5 that was installed while still running macOS 10.4 - - I have no idea whether that matters, or not.
Try a clean install:
1) drag fusion to the trash
2) empty trash
4) empty trash
5) reinstall fusion
Then check system preferences/security for an 'allow' button.
Did that. Still broken.
After the reboot, there was nothing in the trash to empty; the fixed icon in the dock was still there; and when I launched the app, the license key was still in place.
The system preferences - security&privacy shows VMware Fusion in two places (Accessibility and Full Disk Access), with the box already checked in each place.
NOT a "clean install" as I think of those words. Is there some other way to de-install the product that really cleans it out while leaving the VM files themselves intact?
The problem behavior is identical.
Installing the update from 11.5.5 to 11.5.6 that was automatically presented to me by Fusion changed Fusion with four working VMs into a totally unusable state.