To go through what it could be and eliminate what it can't be, there are a number of related words each with different nuances.
You are looking for a single word for a small room that connects to other rooms but has no purpose by itself.
vestibule, foyer, lobby, entrance - These are all near the entrance (or exactly so in one case). A vestibule is a little room right behind the entrance door, possibly to keep cold air out of the rest of the place (like an airlock) or as a coatroom or mudroom. A lobby is a large waiting area, like at the entrance of a hotel. A foyer is an entrance hall, sort of like a very small lobby for a personal home.
A passage or gallery is a long connecting space. It can be inside a building or the space between two buildings or a connecting corridor between two buildings but is covered.
A waiting room is a smallish room that is intended for waiting. IT is superficially similar to the others because it connect other rooms with specific purposes. But it is not simply a connector because it has its own purpose as being a place to wait to get into other rooms.
An antechamber sounds like it is part of a palace or pyramid, a waiting room before the main room
A hall (for at least one of its primary meanings) is (generically) a connecting room that you walk through to get to other rooms. It has the connotation of being longer than it is wide.
A hallway is identical logically to hallway and can replace 'hall' whenever that refers to the room. That is, if 'hall' is used for a building, you would not replace it with 'hallway')
A corridor is a long hallway (which, etymologically, you can 'run' down). It is formally identical to a long hall, but I can only express vaguely that it gives the feeling of being the space of the hall in addition to the function of a hall.
So these are explanations of meaning but it doesn't really do any good unless you show how it might be used for your purposes.
What would you call that place? I'd call it a 'room' (because yes, it feels like 'hall' should be longer or at least less mundane).
For example, how would you tell someone to go replace a fuse in the electrical panel. Where is the panel?
'Go find it in the room between the kitchen and the bedrooms'.
I'd also say 'Go find it in the hallway...'.
But if you're in the bedroom and you want somebody to leave for a moment:
'Please wait for me out in the hall.'
You wouldn't say 'out in the room' because you're in a room already.