Master bedrooms own AC unit

We have a small unit that only runs the master bedroom. There is a hallway that goes to the master with no AC vents, that leads into the living room.

My question is, do y’all think it would be best to shut the master door and let it be on its own throughout the day, or leave it open and help the living room maintain temperature?
Or does it really matter?

I know this summer is almost over and has been a bitch, just trying to get ideas for next year