> Is Dr Horton building homes in Austin?
Yes, a ton.
https://www.drhorton.com/texas/austin
> That could explain high profit while dissuading new construction in Austin.
Given they're still building a ton in Austin, there doesn't seem to be a dissuasion for building there. I do not have any idea about their average margin in the Austin market versus other markets though, but if that was a major decider on whether to build or not the answer is they're still choosing to build.
You can look at new housing starts to see there is indeed a dissuasion to building there. That's literally the very first observation in this thread: construction rates are already falling significantly.