The person we saw was a master of science in physical therapy, and specialized in/had personal experience with concussion rehab. They were based near a ski mountain, and thus a stream of athletes getting concussed regularly.

If you aren't near any skiing, I'd seek out sports medicine/physical therapy folks who work with your local concussion-heavy athletes. Mountain bikers, cyclists, maybe football/rugby, etc.

There is "vestibular therapist" specialty which is physical therapist that specializes in vestibular issues. I had one who helped with vertigo from BPPV and some of the recovery exercises sound similar.

Ie. Institute of Sport, Exercise and Health (ISEH) in London has both a neurologist (Richard) and a physio (Theo) specialised in concussion recovery, and working together. Been very useful for me (guessing you could do some assessments remotely).

Sports medicine is the name of the specialty.

You'll want to look for a "sports medicine specialist" as mentioned