Water stains on the terrace roof coating

For quite some time now, I have been trying to remove the water stains on the coating of the terrace roof, so far without success. What happened: For my almost 14m wide terrace roof, I needed a lot of wood and the preliminary work was done outside at that time. Blue protection, then a layer of sealant on top, and then 2 coats of white paint. The problem is that it probably got too wet at some point and the paint ran down the beams. Back then, I thought: It doesn’t matter, I’ll just paint over it as soon as the thing is standing, BUT either the paint does not cover at all, or the streaks show through again. These have also been visible for quite a while now; it probably isn’t wet anymore. Therefore, the question to the professionals: how can I get rid of these stains? There are obviously a lot of them, and they really don’t look good. Attached is a photo of the mess. I hope someone can provide a good tip.