You are right, but this might just be semantics. Perhaps you already know this, but for others, rent is included in CPI, and for those those who own, "owner equivalent rent" is used as an estimate of the amount of rent they would be paying. Incredibly, the amount of OER is determined by asking the owner they think they could rent out their home! I'd guess that home prices must correlate strongly to this estimation. So while home prices are not directly included, over time, as homes are bought and sold, they sale prices almost certainly influence the CPI, even if they are not directly a component.

Here's the Bureau of Labor Services Q&A on the topic:

"How the CPI measures price change of Owners’ equivalent rent of primary residence (OER) and Rent of primary residence (Rent)"

https://www.bls.gov/cpi/factsheets/owners-equivalent-rent-an...

You're right, housing inflation measurement != house-price inflation measurement.

Not sure how much that distinction really affects the median person though, if housing (rent) inflation is under control. I suppose people with kids may prefer to buy for long-term consistency, so CPI misses them in a way.