This guy analyzed the changes in mailing addresses on credit reports to determine who moved where:

Conclusion

Did the COVID-19 pandemic start an urban exodus? The estimates presented here strongly suggest that migration flows were unfavorable for urban neighborhoods during 2020. However, the word “exodus” emphasizes that migrants are leaving a particular area in large numbers. If we look at the gross flows underlying the trends, we can see that the declines of in-migration are almost always greater than the increases in out-migration. Out-migration did increase in many urban neighborhoods, but the magnitudes probably would not fit most definitions of an exodus. What is certain is that hundreds of thousands of people who would have moved into an urban neighborhood in a typical year were unwilling or unable to do so in 2020. These people may be harder to identify, label, and interview, but they may be best positioned to tell the real story.

Link to Study