You’re getting epicycles confused with long term trends. From your own source:

Price growth continues to be held down by below-normal demand, increased inventory and a return to seasonal price trends that typically begin dropping in the fall.

Also from your own source:

Over that time, rents rose over 11.5 percent, climbing from $1,839 to $2,054 in August 2022. Prices that September were still up 8.83 percent but began a decline — led by decreased demand — which lasted until rents bottomed out at $1,937 in February of this year.

Bureau of Labor Statistics has a 12-month lag when it comes to housing price, which means that elevated rent is still counted in the CPI print.

Yeah, that’s how CPI works. Not sure what point you think you’re making.

Expect to see CPI continues to fall over the next few months. The current round of inflation is over. Expect to see CPI continues to fall over the next few months.

The CPI isn’t falling, so I’m not sure where you’re seeing a continuation: CPI for all items unchanged in October; shelter up

Rents are still up from the trough in February and we’d likely expect a similar pattern to happen next year assuming that the typical pattern holds. We’re still above that bottom from earlier this year and to say that a seasonal cooling off represents entry into a longer deflationary cycle is ludicrous. None of that even addresses (again from your own source):

Over the longer term, rents remain elevated. Since the pandemic, prices have increased by more than 20 percent, adding over $340 to monthly rent bills

All the right wing economists who predicted a scary recession throughout 2022 and 2023 were wrong.

Cool?