Made this comment elsewhere, but CPI is partially derived from the cost of housing, so you can't really use CPI here.
Here's CPI for All Urban Consumers: All Items Less Shelter in U.S. City Average. [1] Index level in August 2019 234.853 Index level in Sept 2023 280.869
An increase of 20%. Very similar to overall CPI.
So rent hasn't kept up with housing prices? Some other anomaly in the calculation of CPI?