Speckled wall after painting - what to improve?

What would that look like? The cloudy areas are filled and roughened? Couldn't quickly find anything on Google

The entire [Kalkzementputz] is fully plastered and only then painted.

ok, I am seriously at a loss. In my opinion, it doesn't make sense to immediately plaster over newly applied plaster, does it?

What is your goal? A smooth, even painted wall? Then you have to fully skim coat the lime-cement plaster! That is really the case. The workflow is skim coating, sanding, primer, then either fleece and paint or just paint. Or do you want a rough wall texture? Then of course you paint the plaster directly, but here too, first primer, because plasters absorb, and the primer as an acrylate first closes their pores. Only the plaster texture, which you call a cloud, will then be visible. You will have to live with that.

I want to preserve the rough wall texture with a reasonably continuous color appearance. I also had to realize that the plaster sucks like crazy. I cannot use acrylate, completely diffusion-open wall construction. I think I will paint a second time and leave it at that.