The academic consensus is that there is a housing shortage, not a surplus. Perhaps there is a local surplus in undesirable areas, but that isn’t true in cities or nationally.
Austin and Texas in general have less housing restrictions than other places wrt zoning and regulation, so they could plausibly have a surplus. You can only really speak locally about any of this because location determines the market
https://www.brookings.edu/articles/make-it-count-measuring-o...