They are most likely mushrooms that are helping to break down the remaining root system of the oak trees that were removed.  I do not think they are causing a problem with a nearby peach tree.

If you could submit pictures of the peach tree that include also include a picture of the base of the of the trunk where it goes into the ground, I can help diagnose the problem affecting the cherry.



Thanks for the additional pictures.  It looks like the soil and/or mulch was on top of the rootball and in direct contact with the trunk of the tree.  With the soil/mulch in direct contact, water was able to be held directly against the trunk.  This allowed pathogens to infect the tree.  Unfortunately we do not have any chemical treatment recommendations. 

If the tree is still alive, you can remove the excess mulch and soil from the top of the root ball to exposed the root flare of the tree (https://hort.ifas.ufl.edu/woody/root-ball-dimensions.shtml).  You then may get a few more years out of the tree, but the tree will never fully recover and will eventually die.  

The Japanese beetles added another level of stress on the tree.

If the branches are pliable, the tree may leaf out again in spring. And if it does, I don't hold out much hope for it living more than a year or two. 

If the branches snap and are not pliable, then the tree is dead.