Hello! Thank you for your question. I’ll tell you about what I use, as well as what I know about parkour shoes in general, but I am by no means an expert on the topic.
First off, as a general rule of thumb, I think that any shoe that feels comfortable to run around in is good enough for parkour, so don’t let not having the “right shoes” stop you from getting started.
My current shoes are a pair of Adidas running shoes (shown below). The bottom is a pretty sturdy piece of rubber, and the tread is pretty regular, but it could be flatter. (I also got them because they were on sale and I liked their colors). In the past I generally use whatever pair of athletic shoes I have, or I get some that feel good and aren’t terribly expensive. One thing that happens with the kind of shoes I use is that the toes can wear out quicker from arm jumps or similar movements. Any shoes, really, that you use for parkour are going to suffer more wear and tear than normal.
I think some things to consider with parkour shoes are the padding on the feet, how light they are, and how the shoe is put together (i.e. flatness, rubber, etc). How much/little you want of each of these varies from person to person. Online, I’ve seen a lot of people recommend Feiyues because they can help you get a feel for proper technique, or Onitsuka Tigers for their grip. OLLOs are another popular recommendation. If you want to try them out then by all means, but I see too many people getting caught up in the shoes, when the exact shoe does not majorly affect one’s ability much more than a different pair would.
Again, I what I do and recommend is just focusing on finding something that is comfortable to train in. If you want some recommendations from people with more experience than me, here are some videos on the subject: