Connecticut Code Chapter 249, Sec 14-299, Para (b):
So if I have a green light, I can enter the intersection. If the light turns red while I’m there, traffic on the other street can enter the intersection but must yield to me.
You were not informed correctly. Of the few states I have looked at so far, every one says that a driver approaching or attempting to enter an intersection is you yield to vehicles already in the intersection. Which makes complete sense, because the point of traffic rules is to keep everyone moving. If you are actually in the intersection, the other cars (which are not oncoming traffic on green) are obligated to let you move out of it. Texas is the same as the other states I looked at.
When I lived there, TX defensive driving was taught by minimally-trained contractors, so the misinformation isn’t surprising..
Also apparently not taught or learned is that Texas code doesn’t grant anyone the right of way; right of way is something you are required to yield. That’s been the case everywhere I’ve lived this far.