looks similar to sepatoria leaf spot, it I believe is a fungus and happens after prolonged periods of wet/cold weather, nothing to worry about IMO.

My loquat gets something that looks like that every Spring and it goes away during our dry summers. I agree with MoleX.
John S
PDX OR

I will treat it with cooper spray.
Lou

You may also want to put up some kind of shade for the first few years. I have one that was in full sun, and it has never grown, gave all kinds of problems. I planted 3 in the edge of the woods, near a hickory tree that I am planning to take down, so it would shade them. They are growing like crazy!

Agree with above that the spots are most likely signs of a fungal disease. The questions to consider are whether this will occur only sporadically under unusually wet conditions and to what degree it is setting back the growth of the tree and whether it will also damage the fruit in the future. Your idea of a dormant copper spray sounds sensible and should not hurt, though it may not be effective and if this proves to be a recurrent problem that damages the plant or fruit, you may need to consider spraying growing-season antifungals. The good news is that pawpaws can most often be grown without the need for this. So for now I would do nothing but observe.

I've had the same beneficial experience with shade and pawpaws, though at Z5 and with a plant that size he may not particularly need it there now. Shading also hasn't fixed all of my various pawpaw's assorted problems. I do not find them easy to grow in the south, short of trying many and accepting a fair number of losses.

The same has happened on my Ruby Keenan every season since I grafted it. It performed best this year through July without leaf spot, but we were also amidst a historic drought with low humidity here in Northwest Arkansas. We've had significant rain since late July, and the leaves are again succumbing to the leaf spot. I'm not sure it's worth keeping this variety. None of the other seven trees have this weakness.