I don't think construction has nearly as much relevance for Austin as you might think. Speaking as a former Austin resident, I left Austin in 2022 because rent highly spiked and I was effectively priced out of where I was staying (my rent spiked in the realm of 40%).

Rent has been cooling off in Austin because the amount of people moving there has heavily gone down and tech companies have either stopped opening new buildings there or have outright started to leave. The huge rise in rents was effectively due to a 'tech speculation' bubble as a result of every major tech company saying they were going to move to Austin and it was going to be the new tech capital of the US.