Plaster house wall sandstone priming?

In an old building, the plaster on the base of the facade is now peeling off in many places. See photos. What is this type of plaster actually called? Is it "Kieselputz" or simply "Rauputz"? Are there also (any?) alternatives to Kieselputz? If you want to plaster the base now, you would probably have to consider that the actual wall is made of sandstone. In order for this sandstone to breathe moisture, a diffusion-open coating would probably have to be used. Am I correct? Which products are suitable for this? Does a primer always have to be applied under the plaster? Or are there plaster products that do without primer? Which priming products are recommended? What should the plastering work (excluding material) cost per square meter?