Solved the problem, reporting back to the community.

/etc/dovecot/dovecot-dict-sql-user.conf had been lacking dovecot group permissions. It was 700/root:root.

However why it wasn't reported by Dovecot explicitly in the log -- the greatest mystery to me. Now, after deleting dovecot and all its packages via 'apt' and installing afresh makes "lacking permissions for the file" entry to appear in the log.

I can confirm that Dict-quota works perfectly well with Dovecot 2.2.22.