The raw edge looks like a gypsum panel (drywall) or it could be as Beverly suggests, a ceiling system that is no longer made. If it's a gypsum panel, it could also be sprayed with a coating as Beverly said.

Ceiling tiles . They were often used in MCM homes and those beams probably added later I had the ceiling panels all over in my MCM ranch and every room had a different one . I left the 2 small bedrooms as is and just painted the ceiling but in the rest of the house we removed them all and drywalled since there was also werd foil type stuff under the tiles a million staples all had to be hand pulled it took me days . If you do not hate them I suggest just paint them the same as any other ceiling . BTW we do have ours tested thye were not asbestos.

They could be gypsum plank roof panels. I've only seen them used on one other building. 2" or 3" thick I believe.

Clean em, prime em, paint em, and be super careful to mask off those fabulous beams and amazing stone wall.

Some sort of Homosote or pressed paper product. Prime and paint (it’s going to suck up primer)

I have that in my house in Florida. It is about 3/4 inch thick and is a fiber-board type thing and is tongue and groove. It is laid on top of the ceiling beams during construction (1957) and tongue and groove roof individual boards underlayment is above that and then the roofing material. I have what they call a "flat roof" even though it has a pitch. It is a post and beam type construction. I had a roof leak and one became badly discolored and took I don't know how many layers of Kilz and paint to cover it. It just kept getting soaked up! My ceiling is exactly what these photos are showing.