Yessssss, got it working.
I uninstalled the extension and program. I uninstalled all the September Windows updates and rebooted. This broke my Start Menu (thanks Microsoft) but the Windows updates seemed to reinstall automatically at some point and fix the Start Menu after a couple reboots. Then I reinstalled Bitwarden desktop app, logged in and set up biometrics, then installed the Edge Extention, logged in and set up biometrics. Then rebooted.
Now the extension prompts for biometrics and the window actually pops up and I can authenticate with my finger.
What a freaking hassle. I suspect Microsoft moreso than Bitwarden. In any case, thank you Nail1684, I appreciate your responses!