This worked for me.
How I got Screen Recording permissions without scripts
Note: Initially I didn't have the option to turn it on in Privacy settings.
Had 11.5 installed
Uninstalled 11.5 with CleanMyMac. You could do this with AppCleaner.
Found a .vmwarevm (probably in ~/Virtual\ Machines.localized) Right click > Open with VMware Fusion
Got the prompt to add screen recording privacy setting
Downloaded 11.5 and installed overtop of 11.1
From reading through comments it seems like a crapshoot this fixes the issue for people. FWIW this worked for me.