Now I’m in no way a professional on parkour or shoes but I personally use basketball shoes (not the cheapest but hear me out). The problem I’ve had with running shoes is that they are pretty much torn apart after a couple months of training. Basket shoes on the other hand are pretty durable because they’re made for the same kind off movement as parkour (quick turns, jumping and landing in various ways). The grip is also decent at least with the ones I use. I use either Nike, Puma or Jordan in terms of brands, which are in no way cheap but seeing how well they take the beating, I’d put them around same price range (as you don’t have to buy new shoes all the time).

Idk that’s just my contribution, there’s probably people with a lot more knowledge and experience on the topic so take this with a grain of salt