Hard to tell what is causing the non-recognition of your DSR-11.
Non-recognition frequently is caused by a defective or loose cable connection, or a defective socket. So, you might check out those issues. What exactly is your cable and adapter setup, from the player to your Mac?
Not sure whether the Image Capture app is still available with Big Sur (look in the Applications folder). If it is available, try seeing if that app will recognize the DSR-11 and, if it does, try importing to your Mac instead of directly into iMovie.
You might also try getting the player running before starting the import process and see if that will trigger recognition.
To rule out some software isues, try these three diagnostic procedures:
Deleting Preferences
Open iMovie while holding down the Option and Command keys and select to delete preferences in the box that appears.
iMovie will open in a new library. Reopen your old library to get back to your projects. Deleting preferences is a safe procedure that will not cause data loss or disruption to your project.
Resetting
the System Management Controller
Try resetting the System Management Controller (but no longer available for the new M1 computers):
https://support.apple.com/en-us/HT201295
Resetting the NVRAM or PRAM
Try resetting the NVRAM or PRAM.:
https://support.apple.com/en-us/HT204063
-- Rich
