along with this, I always use a hammer to tap my T handle(holding the bit) gently as I apply the unscrewing pressure. the tap really helps free it up as you unscrew. never stripped a screw/bolt since I started doing this.Depending on how stripped the head is you can try using the next size torx up and using a hammer tap the torx into a good seating depth. You can try the same with a Allen wrench.
I’ve had luck with speciality removal tools before...even in really tiny screes that I thought were hopeless
The other thing that works is still bits that are cut the opposite way...forget what they are called though
unplugged