Thank you for sending this question to "Ask a Master Gardener".  Your pics were really helpful in my search.  I 
used images to locate similar damage to plums.  This first site had the best match.
https://www.armuro.com/en/plum-tree-pest-disease-treatments/

Shot-hole disease (Stigmina carpophila)

The disease is common in untreated orchards and causes significant damage to stone fruit trees. Circular spots appear on the leaves and the tissues turn brown and eventually detach from the rest of the leaf. Punctiform formations appear on the fruit, surrounded by a purplish-red border. The fruit pulp loses its texture and taste. The fungus causes browning of the fruit, followed by wounds. This form of attack is very dangerous because it dries out the fruit buds. The spores spread the fungus and resist over winter in the sap that drains from the wounds. The fungus can also overwinter as mycelium on the branch’s surface.

Prevention and control measures:

• pruning and burning the affected branches;
• covering the wounds resulting from prunings with tree wound sealer;
• after pruning, treating the plum trees with Bordeaux mixture;
• preventive treatments in vegetation with specific fungicides.

Plum fruit moth (Cydia funebrana)

This species attacks stone fruit trees. It develops two generations per year and overwinters in a cocoon under the bark of trees or in various sheltered places. The larvae penetrate the fruit and feed on the pulp and seeds. The attacked fruits stagnate from growth and fall. The larvae continue to feed on the fallen fruit. After feeding, they come out of the fruit and look for the right place for winter.

Control methods:

• chemical treatments with specific insecticides.

This site is more hopeful, but I am not sure the fruit damage is not the same.

rost pocket and the tree will survive but fruit will suffer.

PLUM SAWFLY

The picture above shows the damage done to plums by the plum sawfly (Hoplocampa flava). From the outside the plum looks OK, may be a small brown mark on the skin but nothing more. But inside, the plum is completely inedible. You may also notice one or two small hardened drops of resin on the fruit which are the tree’s response to being attacked.

In spring the sawfly emerges from the soil and lays eggs on the blossom of plum trees. When the plums develop the little caterpillars eat their way into the centre of the plum and feed off it as the plum develops.

Plum Sawfly is difficult to control using organic methods, the only one being available is a pheromone trap which goes some way to controlling the disease.

Look for the giveaway brown mark on fruits and when they are forming pick the fruit off and burn them, this will help in controlling the disease next year. Burn any fallen fruit which is unusable.

You did not mention leaf damage in your question, but I included this site in case it is relevant.
https://extension.psu.edu/plum-disease-plum-leaf-spot

Leaf spot of plums and prune-type plums is caused by the fungus Blumeriella jaapii (formerly Coccomyces prunophorae).Save for later Print

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Updated: April 8, 2023Skip to the end of the images gallery

Source: Joseph OBrien, USDA Forest Service, Bugwood.org

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The fungus, its life cycle, and the disease it causes are very similar to those of cherry leaf spot. On plum leaves the spots tend to be smaller, and severely infected leaves often have a tattered appearance. Unlike cherry infection, severe plum leaf infection is often followed by a heavy fruit drop.

Disease management

Most cultivars are susceptible to the disease, so fungicide sprays along with the sanitation practices suggested for cherry leaf spot are necessary for control. A light disking should be done just before overwintered spores on leaves are ready to be discharged, about the time of shuck fall.

I hope this info will steer you in the right direction.  Please let me know if you have any other questions.