The problem was using the wrong configuration property name “publish.full.document.only.tombstones.on.delete”.
The correct property name to use is “publish.full.document.only.tombstone.on.delete”. And with this setting, it works as documented.

This was pointed out to me when I created the ticket [KAFKA-417] MongoSourceConnector v1.12.0 does not produce tombstone messages - MongoDB Jira.

Posting reply here so that the community is aware.