Most people with TOS should try Postural Restoration Therapy before considering surgery
Unless you know specifically that your underlying TOS root cause is something like an extra rib that requires surgery, I highly recommend locating a PRT (postural restoration therapist) near you to help manage your gait and functional posture.
I've posted here before, but I'm someone who spent/wasted countless hours being told by doctors and standard PT trainers that my hip, breathing, and arm symptoms couldn't be related as different muscle groups. It was only with my own research and using AI that I was able to learn about the concept of PRT and I found a professional who has helped give me my life back.
In fact, I'd say I've not only recovered, but I've improved mobility even beyond what I thought was recovered. In my case, hypermobility and weak core / glutes resulted in severe guarding via hip flexor muscles. This ultimately twisted my ribcage and hips to the point it was cutting off the Thoracic opening while also preventing my diaphragm from proper expansion and contraction.
Ultimately the cure/treatment was just a few band workouts highly focused on proper form. Much more successful that traditional PT and 20+ drills you're expected to remember.
Feel free to PM me if any questions!