I have been using iMovie 10.3.1 on a 2015 13" MacBook Pro to import DV footage from a Sony DCR-PC9 with no problems (4 pin to 6 pin FireWire cable > Elago FireWire 400 to 800 adapter > Apple FireWire 800 to Thunderbolt adapter > Mac) using Big Sur. As soon as I updated to Monterey, I can confirm the camcorder no longer displays in iMovie's import window. However, in System Information the camcorder is still successfully identified.
Using another Mac (a 2020 13" MacBook Pro) running Big Sur, I can still see and import the footage in the SAME release of iMove, 10.3.1 (this time with adding the Apple Thunderbolt 2 to Thunderbolt 3 adapter to the end of that already hilarious adapter snake). It really does seem to be a specific part of Monterey that broke some DV equipment being recognized by apps.
I had even played around on Big Sur and used the same camcorder as a webcam in Zoom with no issue and can confirm Monterey broke that as well. Given the system is having no issue seeing the full device tree, I hope a simple update can fix this for those of us with legacy creative workflows.
P.S. Because of this issue, I had to run my last import on a 2005 12" PowerBook G4 in Final Cut Express and transfer it over with a CF card — I kid you not!