Incoming email does not process the mails

I switched the Incoming Mail feature from IMAP to Microsoft Graph. Now, emails are not processed any more. In the mail_room_json.log I can see that a connection is established, the mails are read/processed but they don't appear in GitLab. Both the Incoming Mail feature as well as the Service Desk feature are affected.

Log extract:

{"severity":"INFO","time":"2022-10-09T11:41:52.855+00:00","context":{"email":"incoming@mydomain.loc","name":"Inbox"},"action":"Getting new messages","unread":{"count":1,"ids":["BBMkaGJiMjU4YWQ4LTRmMjktNDc5Ny04OWVjLWM5Nzg0ODdhZTlhYwBGAAAAAACuekkRdigHRK9q9ZzA9UvoBwAsMiJ-1pBfS6QTwOZ18V0DAAAAAAEMAAAsMiJ-1pBfS6QTwOZ18V0DAAGfFWgMAAA="]},"to_be_delivered":{"count":1,"ids":["BBMkaGJiMjU4YWQ4LTRmMjktNDc5Ny04OWVjLWM5Nzg0ODdhZTlhYwBGAAAAAACuekkRdigHRK9q9ZzA9UvoBwAsMiJ-1pBfS6QTwOZ18V0DAAAAAAEMAAAsMiJ-1pBfS6QTwOZ18V0DAAGfFWgMAAA="]}}
{"severity":"INFO","time":"2022-10-09T11:41:52.936+00:00","context":{"email":"incoming@mydomain.loc","name":"Inbox"},"uid":"BBMkaGJiMjU4YWQ4LTRmMjktNDc5Ny04OWVjLWM5Nzg0ODdhZTlhYwBGAAAAAACuekkRdigHRK9q9ZzA9UvoBwAsMiJ-1pBfS6QTwOZ18V0DAAAAAAEMAAAsMiJ-1pBfS6QTwOZ18V0DAAGfFWgMAAA=","action":"sending to deliverer","deliverer":"MailRoom::Delivery::Postback","byte_size":4083}
{"severity":"INFO","time":"2022-10-09T11:41:52.937+00:00","context":{"email":"incoming@mydomain.loc","name":"Inbox"},"action":"Quitting connection..."}
{"severity":"INFO","time":"2022-10-09T11:41:52.938+00:00","context":{"email":"incoming@mydomain.loc","name":"Inbox"},"action":"Terminating watching thread..."}
{"severity":"INFO","time":"2022-10-09T11:41:58.972+00:00","context":{"email":"incoming@mydomain.loc","name":"Inbox"},"action":"Setting up watcher"}
{"severity":"INFO","time":"2022-10-09T11:41:59.241+00:00","context":{"email":"incoming@mydomain.loc","name":"Inbox"},"action":"Retrieving OAuth2 token..."}
{"severity":"INFO","time":"2022-10-09T11:41:59.509+00:00","context":{"email":"incoming@mydomain.loc","name":"Inbox"},"action":"Processing started"}

Since the logs say sending to deliverer I would expect everything to work fine but that does not seem to be the case. Where else would I need to debug to figure out what's going wrong?

Running the command gitlab-rake gitlab:incoming_email:check returns the following output:

Checking Incoming Email ...

Incoming Email: ... Checking Reply by email ...

Mailroom enabled? ... skipped
MailRoom running? ... skipped

Checking Reply by email ... Finished


Checking Incoming Email ... Finished

EDIT: We are using GitLab 15.4.2-ce.0 (via the Docker Image from Docker Hub)