Some kind of scale insect?

Yes, I have similar things on oak trees, it doesn't seem to be a problem.

{{gwi:125702}}

A sweet substance must be there in the early stage, [food].

Konrad, you have oak galls. The wasp is a carnivore looking for some meat. If the galls are still there, cut one open. You likely will find a tiny white worm, the actual gall. The Persimmon looks like it has scale. The ants farm the scale and eat the sugary drops they make. Nature generally keeps both pests at a low level.

Galls rarely hurt the oaks (can kill small branches), scale are a time bomb waiting for conditions that allow them to explode their populations. Persimmons shed copious amounts of small branches, and since scale are usually only on small branches, they get shed along with the wood.

Thank you Dzitmoidonc,.. good to know!