posted 6 months ago
Sounds like bacterial spot. I have this on my peach tree. The gummy "exudate" is a good sign and I can see your leaves have the "shot hole" pattern.
I think there might be some organic copper sprays but I haven't tried anything for control yet so I can't speak to that. I think you often have to have very accurate timing with sprays for them to be effective, and I'm just not willing to make that time investment at the moment. As far as I know, the infection doesn't hurt the tree itself much, so how much effort you put into control depends on how much you care about the effect on the fruit.
For me the severity of infection seems to vary a lot from year to year. Last year was terrible. This year, despite being extremely wet, it's looking like it will be pretty mild. When the infection is bad, it doesn't spoil the fruit but it can give the skin a very unattractive and unpleasant rough texture. If you're peeling and preserving, it's not too big a deal. It definitely makes them less appealing for fresh eating, though.