We have an old 1950's house with that old fiberboard on the walls. We had a bad corner I have fixed and now need to try to texture and blend the fix back into the pattern. I cannot seem to find just what would make this texture in the picture.
i'm not positive ,but it looks like a sand texture paint.you get it at the big box or a paint store ,about 5 bucks then mix it with your paint and roll it on .youl have to play with the amount you put in the paint to get it right just rember you can always add but you cant take it away
You should lay down a bonding primer so all you come up with has something nice to adhere to as you go forward.
My guess is sand and lots of coats of paint. You might try the bags of polystyrene pellets texture at the paint store too. They offer more texture with less weight than sand or gravel. Experimenting to match is the key. Make sure you work in small batches and not the original paint can. Make notes of your formula so you can replicate it. Stir often to suspend the texture.
You might try mixing the texture in thinned drywall texture to bulk it up. Then prime and paint over it.