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.
For me changing the VMware Memory settings didn't help. The key was to give Screen Recording privilege to VMWare in the macOS System Preferences > Security and Privacy.
Since VMWare didn't appear in the list there I followed the steps from this post:
Thanks a lot posts.boy!