I upgraded to the latest version 3.9.9 and then it worked. There was a message at the beginning about some problem with files.
I will have to explore it and trim some excess bagage from it.
The database was probably copied/migrated while it was indeed in use by DEVONthink on the old Mac and that caused both this warning and (some of) the errors.
Missing files are logged to Window > Log. Are these indexed items?
I am pretty sure that DT was closed on the old machine before I copied the files. The windows log is now empty.
Except for webclippings I would say that everything else is indexed.
I made a mistake when I first got DT to put everything on my Mac into the database. I will have to delete everything except webclippings and start over.
Note: You already have a support ticket open on this issue.