That sounds like a really good observation- that you note instability on one leg and also some odd foot function. It’s definitely worth a check – but make sure to find a PT that has specific focus with this – not all are created equal. Where do you live, generally? Might be able to recommend someone to you!
If you want to do a little more self-assessement or background reading, a PT wrote a book that can be quite useful for this- check out Jay DiCharry’s “Running Rewired”, specifically pg 77-88 that talks about foot function and single leg control. (I’m a PT too, disclaimer). Info in there translates nicely to mountain sports and compliments much of the strength and movement patterning work that Uphill Athlete folks have put together here.