For a point of reference, I had no problem testing the mounting of a Veracrypt (v1.24-v8) volume using FUSE 4.2.1 under macOS 12.0.1 (Monterey) upon seeing your post. (I installed Monterey last week and hadn't even thought to test VeraCrypt but I'm glad you mentioned it. ;-) )
In my case, I was prompted to re-authorize the FUSE extension during my first attempt to mount, however. It looked like this:
And then this:
So I opened Security Preferences, unlocked the control panel with administrative rights (padlock) and then clicked the Allow button.
It prompted me to restart (as the first notification window suggested), then I re-opened VeraCrypt and mounting works fine.
If you did not go through a similar set of steps, I'd suggest researching FUSE system extension permission related fixes. This does not appear to be a VeraCrypt issue.
Hope that's at least helpful in pointing you in a direction. Best of luck,
Brian