Since this morning (not sure, seen first time this morning), I cannot connect to CardDAV any more. It used to work; yesterday I switched to Two-Factor-Authorization. After the first problems this morning with the contacts, I set up an app password (something I forgot yesterday), but this does not work. CalDAV seems to work with its own password.
CardDav issues are not related to the contacts app!
Moving on 2FA
I have the same problem. 2FA doesn’t seem to work with caldav and carddav accounts. I had to disable 2fa to enable synchronization again.
How should a 2FA authentication work when an app access is required? You have to create individual “app passwords” for the apps, if you want to continue to use 2FA for the interactive login.