Each side of the connection has its own workflow, and you are only interested in the fact that the remote issue has changed status. This change should have no effect on the local status, but actually, be converted in a comment.
This is pretty straightforward to do with a change processor.
First, you need to ensure that the status information is included in the replica:
In your change processor you can add a comment whenever the status of the remote issue was changed:
Here is how the result looks in your Jira: