Recently what appears to be a bug has been reported re the inability to recognize a DV device after upgrading to Monterey 12.3.1.. If it is a bug there is no solution until Apple fixes it.
If you have a time machine backup you possibly could revert to your previous operating system. If you try that, back up first.
The only way that I know of to revert to an older iMovie version is to use your Time Machine backup to revert to the earlier version. However, if you have opened the iMovie library with the newer version, it won't open in the older version. So you might need to restore your older library as well.
Before reverting to an earlier iMovie or OS, since the Mac is recognizing the carmera try importing into QuickTimePlayer instead of iMovie.
Since I have never restored earlier iMovie or OS version myself, you would be safer to call Apple support and have them walk you through the process. You can contact Apple Support by clicking on the Get Support item in the upper right hand corner of this forum’s screen. Navigate to a place where you can enter your phone number.
-- Rich