I think you stripped the Torx head, not snapped off. Did you get the socket on the bolt head snug and tight during the work, or kind of loose?Stupid me; took a long bar and try to remove, due of this action bolt top of bolt head is snapped.
In this case, with rusted bolt, I would use the impact driver with a Torx socket and hammer on the bolt, but make sure the driver is set in the CCW direction correctly:
The hammering action will loosen the bolt threads and it will eventually turn.