@swamidass is correct, getting “M” is just a matter of data-fitting. Note however, that non-GR black holes or even non-black hole objects can give a good fit (though we won’t know if this fit actually returns the mass of the object).
Exactly; Einstein made the prediction, not the many legitimate scientists who work on the EHT to fit the observation with models that include, among them, Einstein’s prediction.
It’s like this: If I have a bag with between 1-3 marbles in them, then I ask: “How many marbles are in the bag?”
Newton says: 1
Einstein says: 2
Crackpot says: 3
These are predictions.
What the EHT is doing is the following: to answer “How many marbles are in the bag?”,
Make the model that each marble is 1 gram each and weigh them. They can then fit for the number of marbles in the bag based on this model.
Suppose they get N=2. This number of marbles that the EHT came up with from this procedure is not a prediction. Nowhere in this procedure did the EHT team did any prediction. They can then say: Einstein’s prediction was right. But they themself did not predictions.