Getting your mail out
Over IMAP, the same way you read it. Any mail client can pull a full local copy of every folder, and that copy is yours — there is no export request, no queue and no waiting for a file.
Thunderbird is the usual recommendation for a bulk copy because it handles large accounts without complaint. Apple Mail and Outlook will do it too.
Leaving is a DNS change after that: point the MX somewhere else and mail stops arriving here. The domain was always yours, which is the part that makes the exit real rather than a promise.
Did this not answer it?
Mail reaches a person rather than a queue. Include the domain and the exact error if there is one — it saves a round trip.
sales@ruber.me