Sometimes we just have to try things and take it day by day to see if you feel better or worse.

But if you feel uncomfortable with what the PT is wanting you to do, or if you are getting worse, say no and hopefully they will listen.. and make adjustments to the PT plan. If not walk out.

Stretching + hyper mobility is a fine line, you don't want to over extend yourself.
And some muscle tone does help to balance & protect the lax joints.

Does that PT place have expert /advanced team?
Maybe they could each evaluate you and compare notes??

I'm assuming you had x rays / MRI to rule out any obvious things.

Do you know how you acquired TOS?
Repetitive work or some other injury - sports , car accident etc?