It’s always a little hard to tell from pictures, which is probably why there are so many diagnoses on this thread, but I’m not sure I see borer evidence.
I see the sap spots, but don’t see any on the lower part of the trunk. The major peach tree borer attacks the lower part of the trunk, or the roots. There is a lesser peach tree borer (and another borer) which attacks higher parts of the tree, but that borer is much less common in the NE, and the borer generally attacks wounds and crotch angles of peach trees, not the smooth bark. I think the “bleeding” spots I see are simply spots where the bark is dying underneath.
Your tree does have canker, but like Scott, I have trees which are worse than yours. It’s more problematic that your tree has so much dead bark and lacks vigor. It can be hard for the tree to heal when there is a lot of dead cambium tissue. Even though the bark looks sound from the outside, it can be dead underneath and show up the next growing season.
Nevertheless, sometimes peach trees can recover to some extent from lots of dead bark, or at least continue to produce for many years.
I would definitely avoid trying to cut out canker on this particular tree, unless you are going to try to remove dead limbs. The tree looks very weak to me, and trying to remove places of bark might do it in. Instead, I would try to improve the vigor of this tree.
Here are some things to try early next spring.
Start by removing a larger weed free area underneath the tree. I recommend at least a 6’ radius of weed sod free area for your tree. You could do this by hand with a hoe, or a careful application of Roundup (careful not to get any on the trunk or foliage of the tree) or using a light organic mulch. Peach roots don’t compete well with sod, unless the trees are larger and healthy.
Secondly, I would apply some nitrogen fertilizer to get the tree growing well. Well growing peach trees are much more capable of fighting off canker (or living with it) and heal larger areas of dead bark. A generous amount of N fertilizer will result in substantial new growth. You can overdo it with fertilizer, so you might check back with the forum when you purchase the fertilizer, to get some recommendations on how much to apply of your specific fertilizer.
Lastly, I see some spots on your new shoots, these are probably either scab lesions, or bac. spot lesions (probably scab). You might consider spraying a little captan early in the growing season to control that. But, by far the more important things would be to remove the sod around the base of the tree and apply some fertilizer.
Lastly, I see a place where a branch is crossing another and rubbing. You might cut that out so there is no rubbing, but I would wait till spring because the tree is so weak. As Gsims mentions, fungal peach canker is most active in the fall or winter, which is another reason not to prune your tree right now.