Not sure what to make of that. I can’t replicate your issue. When I connect my AirPods Pro to the Mac, they do show up as a selectable microphone for QuickTime Screen Recording.
If a restart of the Mac doesn’t fix it, then try some generic Mac troubleshooting.
- Start up your Mac in Safe Mode to exclude non-standard software from interfering. If the issue goes away, then some startup item was likely the cause.
- Start up your Mac in a different Mac user account. If that changes behavior, then the issue is likely in some Preference setting or other user-centric property.
What is your model Mac? What is its version system software? About System Information on your Mac - Apple Support
If the issue persists, then I would suggest to contact an expert from the Apple Support staff for further assistance. Contact Apple for support and service (phone numbers) or start your support request online (chat/email/callback).