Weight-lifting
This seems an obvious one to avoid, but . . . .

Prior to TOS, I performed 3 full body weights sessions per week, using the Hypertrophy Specific Training (HST) method and free-weights (bench, squat, deadlift etc). When I began to cease activities as a precautionary measure against worsening symptoms but prior to diagnosis, weight lifting was the last thing I stopped. This was partly because it is the thing I wanted to keep the most, but mostly because with one outlying exception, this never appeared to have any impact on my symptoms.

Advice against resistance exercise for TOS-sufferers seems to be consistent. However, after a 2 month break I have started resistance exercise again, but limit this to my lower body and core region. I do wall squats, leg extensions, leg curls, seated calf raises, back extensions and bicycle crunches. I can detect no negative outcomes during or after such sessions.

Yoga
I'm happy to see a few others already mention yoga. I'm currently practicing yoga each day now. It has somewhat filled the gap created by the cessation of cardio and weight-lifting. As a complete beginner, I do have to be selective about which poses I perform and which I avoid. For example, eagle pose, which involves interweaving your arms and bending elbows, is out because it does irritate my ulnar nerve related complaints.
Of course, corpse pose is always very welcome