Certified GKH Gardening Expert
Ah! This is a much better look at the tree in question. This is, certainly, a cherry. It appears to be one of the edible cultivars. Test a small amount of fruit with your tongue, first. If it has a palatable flavor, then you can test a single fruit. If it produces no burning or nausea, then you can eat some of the fruit with caution.
Spread this testing out over a few days to avoid any issues with the Hydrogen Cyanide content of the tree.