Population has receded slightly in the last couple years in Austin proper, is still greater than 2020, and the metro area has not shrunk year over year at all, although growth has slowed.
Population by year:
2019: 978,763
2020 high estimate for Jan 1 (996,369) - https://austin.culturemap.com/news/city-life/01-15-20-austin...
2020: 961,855 (Census, low mark)
2023: 979,882
2024 (estimated high mark): 986,928
So yes, the population cratered from a high in early 2020. This brought down prices with a 2 year lag, as owners started to get rid of empty units. The prices will come right back up now, that the population is recovering.
A low-single-digit push to local burbs happened all over the country. "Austin" in the same way people discuss "Houston" or "Chicago" i.e. the local metro area has grown every year.
The suburbs migration IS the point. The suburbs are a superior model when it's made possible by de-urbanization of workplaces, and it shows. The price in the suburbs of Austin has been growing.