Inflation does include home prices.

https://www.whitehouse.gov/cea/written-materials/2023/04/27/update-on-housing-inflation-in-cpi/

In contrast, however, housing’s contribution to inflation has significantly increased. Housing now accounts for a third of the consumer basket of items measured in CPI, so even small increases can have an outsized impact on inflation. Last June, housing accounted for a fifth of inflation, contributing 1.7 percentage points. By March 2023, housing’s contribution rose to 2.6 percentage points, making up half of annual CPI inflation. For perspective, before the pandemic housing would typically contribute about 1 percentage point to inflation.

CPI is the standard inflation measure you see in headlines.

What I think you might be getting a is a change to how housing prices were included in 1983. For homeowners, they use a method of calculating how much they would pay if they were renting their home from a landlord.

This sometimes gets misreported as housing not being included in CPI, but that's not true. This method does have its critics, to say the least. However, it doesn't seem to be absurdly off, either.

https://www.fullstackeconomics.com/p/why-the-government-took-home-prices-out-of-the-consumer-price-index

After doing this research, we believe the critics of current BLS methodology are partly right and partly wrong. Today’s annual inflation rate likely would be a few percentage points higher if the BLS were still using its pre-1983 methodology for shelter inflation. But it’s not true, as many people claim, that the switch led to systematic understatement of the inflation rate over the last 40 years.

“We didn’t find that inflation was on average higher or lower with the old method,” said economist Jonathan Hazell, one of the paper's authors. “Rather, it was more volatile for reasons that didn’t make much sense to us.”