It looks like the Berkeley Database with credentials of all mail accounts is missing. The database should be recreated. Use Plesk utility mail_auth_dump:
~# /usr/local/psa/admin/sbin/mail_auth_dump
~# file /var/lib/plesk/mail/auth/passwd.db
/var/lib/plesk/mail/auth/passwd.db: Berkeley DB (Btree, version 9, native byte-order)
~#