OK. I found out what the problem was. I have two user accounts on my MacBook Pro, one is an admin user I almost never use, and the other is a normal account I use all the time.
Three days ago I logged into my admin account to do something very simple. Then I logged out and back into my regular account. But what happened is that I triggered an iCloud Drive sync on my admin account which did not finish. So the message, "Time Machine cannot back up because some iCloud Drive files have not finished syncing," had to do with the iCloud Drive sync on my admin account. Not iCloud Drive sync on my regular account.
I logged back into my Admin account, turned off iCloud Drive on that account as I don't need it there, and when I logged back into my normal account, Time Machine backups work again!!!
So, if you have more than one user account, this could bite you if an iCloud Drive sync has not completed on another account. It will block Time Machine backups from starting no matter what account you are logged in as. And if your logged in account shows that iCloud Drive is in sync, it might drive you insane.
This makes sense as Time Machine backups backup the entire Mac.
The message should be clearer. It should say something like, "An incomplete iCloud Drive sync on xxx account is blocking Time Machine from starting." That would give you a clue that the problem is with the other account.