The basic meaning of hatta is to mark an endpoint to which a preceding action may extend. The endpoint is the point where the relevant course of action is brought to its limit.
«حتى: للغاية في أصل الوضع»
Hatta is originally assigned to indicate a limit or endpoint.
Example: “Travel until you reach the city.” The activity of travelling can extend up to arrival; hence this is the primary endpoint sense, not an alternative-choice sense.