Is there a way to make the Ticket id and Summary be part of the Success reply subject in the mailbox rule?

Is there any way to make the Incident id or Request id and Summary be part of the reply subject in the mailbox rule? Ie. subject "(id<123456>) - <summary>" ?

No, this is not possible. When a new mail arrived at the maileater, it just replies onle the Success or the Failure message.
At this stage the Incident or Request is not yet created, so ServiceDesk cannot reply with the Incident or Request number.
But "one second" later, the Initial Notification is triggered. And this Notification contains the Incident number in the subject line, so the user can reply directly to this Notification.

 Because the Initial Notification is sent anyway, the limited Success message is not used by many customers.