I believe this is happening because the Catalina install is corrupting your local keychain cache.
The only thing that worked for me was to completely refresh my local keychain by wiping out the local keychain directory.
In: ~/Library/Keychains, I moved aside my keychain directory (the directory with the long string of hexadecimal numbers, safely, by renaming it to <keychainID>_save), then rebooted.
Back into AppleID preferences, the "Keychain" option was unchecked. Check it. Enter your passwords a few times, then let things sync up again. From that point forward, everything worked just fine.
This is a pretty extreme solution, but for me, it worked.
\marc