When ours had the same problem, we put organic, cold presses neem oil on the leaves. It stopped the problem right away & kept it stopped even after we quit putting the neem oil. I suppose the bugs found a new home.
It doesn't kill pollinators unless they are directly sprayed or aspirate it while misting. It won't keep the pollinators away. I've seen bees & butterflies show up & do their flower dancing joy shortly after applying the neem oil.
Unfortunately, I think some insects are killed by neem oil. (Helpful or pesky, they are on earth for a purpose so I'd prefer not to kill them- just chase them away.) Many pests just are detracted, so they simply avoid the area. Rabbits must not like the taste or the smell. They stopped eating the plants with neem oil.
For fungus & mildew, thanks to helpful advice I received here, we put it on both sides of the leaf. It certainly stopped powder mildew.
The downside is that neem oil rinses off rather easily. After a rain feel a leaf between your fingers. If it's oily, the neem's still there. It does rinse off easily if it gets on an edible leaf, such as spinach and it leaves no taste behind.
Hope This Helps!
Paul