I know nothing about this, so I guess I'm asking "why can't we do this?": take some brain, throw it in a blender, and look for DNA the same way the ancient environmental DNA people do?
You can't find out this way. Removing brains exposes it to an outside environment where there are microbes. You can't tell if they arrived before or after you removed the material.
Maybe the first point you make is also the argument for why our brain might have a microbiome, as our body is not in any way hermetically enclosed, and e.g. amoebas are able to infect our brains just by going through our nose.
More nitpickfully, one of the big things we care about is if the bacteria are living _harmlessly_ in the brain. i.e., site of microbes, and a lack of inflammation, will answer more than just "are there microbes around".
Place body in sterile isolator, expose dura mater, DNase treatment of the area, insert sterile syringe into brain? Repeat experiment several times, and also process negative controls.
Not my area. I guess the fact that it hasn't been done proves it's way harder than I'm assuming it is.
Related recent story about earth microbes colonizing what was hoped to be a pristine sample of astroid captured in space: https://www.space.com/ryugu-asteroid-sample-earth-life-colon...