The problem that the TaskQuery object was not serialized/deserialized to/from JSON and persisted in the database was that the property wasn't added into the JsonTaskQueryConverter class. I added it and added some tests to confirm that it is working.
It is now possible to send a POST request on /filter/create and create a filter using assigneeIn. The selected assignees will be available if a GET request is sent on /filter, or a PUT request on /filter/FILTER_ID with an updated filter in the request body.
This is the commit, since it's not shown in Jira for some reason: https://github.com/camunda/camunda-bpm-platform/commit/27a8adadfbc22001b557221bde37869f269b6653