Thank you for your question about your birch tree's infestation. Yes; you certainly have evidence of the bronze birch borer. As you can read in this Extension article (and see in photos very much resembling yours), "Treating trees with insecticides to kill borers is only effective if the tree is in the initial stages of decline and dieback. When over 40% - 50% of the canopy has been killed by borers, the effectiveness of insecticides is greatly diminished and a treatment should not be made."

Before proceeding further, I would suggest hiring a licensed, insured, bonded arborist to evaluate the health of the tree and specifically the canopy, and get his/her recommendation.  As the UM article points out, if chemical treatment is thought to be helpful, having a commercial pesticide company involved will be necessary.

I hope this information is helpful to you.  Good luck!

Any chance it might be woodpecker holes? How does one tell? Thank you!

Good question!  The differences are rather obvious when you put them side by side.  Woodpeckers are linear.  Beetles are all over the place, and have a distinctive staining near the holes (which appears to be just above your fingers in the photo.)