Hello!
iCloud Keychain was turned off. I've turned it on and power cycled my phone and I still do not receive a prompt for FaceID from Notes. Should note that the issue is not that FaceID doesn't work for Notes, it's that I am no longer prompted to use FaceID for Notes (it's not even an option)
FaceID works everywhere else regularly (Apple Pay, Apple Card info access, and unlocking my phone are the only use cases for FaceID if I can think of that I regularly use and they all prompt me for FaceID automatically and work properly.)
The default account for Notes has not changed but I did sign in and out of my iCloud on my device after the update as I also lost some of my contacts with the 14.2 update (another issue I've considered posting about but haven't gotten around to.) That said right now I'm signed in on my iCloud account and the correct default account is listed.
Lastly, Notes are enabled in iCloud -- that was the first place I checked :/