The doors don't auto-close on copy-pasted buildings unless you remove them all and re-add them. :-( I don't know when this behaviour started unfortunately as I've only just noticed it, so it could be months.

AutoDoors will not act on doors without an OwnerID, you must set EntityOwner to true in CopyPaste's config under Paste Options.

That did it! Thank you. Now I have to think about why did I set the EntityOwner to false? 😔🤦 I vaguely remember having to do it for another plugin.