I have made this suggestion before as well. The current terminology is confusing to guests.
If you read the descriptions, these tiers are meant to indicate the level of privacy in the listing.
Shared Room = No private space
Private Room = Some private space, some shared space
Entire Place = Fully private space
Unfortunately the names they choose for these make it sound like it indicates the size or layout of the space, not the privacy level.
My suggestion is that AirBnB should simply rename these categories to privacy tiers and name them as Fully Shared, Partially Private, Fully Private, or similar.
You have your situation where you have more than one room, so you don't want to call it merely a "private room," but because it is not fully private that's where AirBnB thinks it should go, and this possibly costs you guests who are looking for more space if you list that way, but conversely possibly upsets guests who are looking for more privacy if you list as "entire place."
I have a similar situation where I rent a fully private but very small studio. It is one room with an en suite full bath and no kitchen (just microwave/fridge/coffee maker, like a hotel room), and the only entrance is a fully private one. I list it as "entire place" because it is fully private, but I have to go to great lengths in my listing to make it clear how small the space is and that it lacks a kitchen so that I don't end up with guests who expect a full apartment and then leave me poor reviews when it turns out reality didn't match their expectations.
The privacy tiers should have names that reflect they're talking about privacy, not size or layout.