If you used the Migration Assistant to recover your VM, the OS permissions that allow the kernel extensions to be loaded probably were not brought over. The kernel extensions will need to be re-registered - that's usually done with an installation.
Unless you have an active contract, Broadcom won't let you download old versions of Fusion from their public download site even if you have a license key for it. But there's a "back-door" location that the VMware products use to download their updates - that's still active. Here's how I would proceed (and I just checked this out on a Catalina installation).
Before doing anything, make sure you have a copy of your VMware Fusion 11 license key. This process wipes the licensing information.
Completely delete any Fusion implementation using the information found in KB article https://knowledge.broadcom.com/external/article/307074/how-to-uninstall-vmware-fusion-manually.html
(this will not touch your existing virtual machines, but will remove the licensing information - which is why you need a copy of it)
Download 11.5.7 directly from VMware's content distribution server https://softwareupdate.vmware.com/cds/vmw-desktop/fusion/11.5.7/17130923/core/com.vmware.fusion.zip.tar
(I tried installing 11.5.1, and updating to 11.5.7 but the in-product updater failed with a certificate error).
Extract the com.vmware.fusion.zip.tar file, you'll find a com.vmware.fusion.zip folder.
Open the com.vmware.fusion.zip folder, and extract the com.vmware.fusion.zip file found there. That will give you a com.vmware.fusion folder.
Open the com.vmware.fusion folder, then open the "payload" folder found there. That should contain the VMware Fusion application.
Move/copy the VMware Fusion application to the Applications folder.
Open VMware Fusion. It should go through the same steps as an installation from the download.