It wouldn't surprise me if the second is closer to the truth. Homebuying is close to where money is injected into the economy: when the Fed drops interest rates, mortgage rates drop, the home price you can afford for a given income goes up, and housing prices go up to compensate (particularly in land-constrained areas like Vancouver or the SF Bay). Other industries like food don't go up until that money has had a chance to circulate through the economy and make it to the average food buyer. I'd expect to see large increases in the CPI over the next decade, with housing last decade being a harbinger.
by saying this, you’re implying that there is some underlying “truth” to cpi and housing prices, but it misses the underlying critique that these measures are not representing the truth on the ground at all, as experienced by americans.
cpi and housing prices may be correlated, but that says nothing about whether they each measure anything of societal relevance (similar to the critique of IQ, for example). we should expect housing prices to correlate to some combination of gdp (or some near equivalent, since that’s also a measure that’s gamed politically) attenuated by population and wages, as those would be underlying ingredients in the supply and demand functions. then when the correlation falters, we could potentially diagnose how the economy might be failing a core function of providing shelter to the populace.
Also, the current level of divergence between housing prices and CPI is nothing out of the ordinary. It will correct itself over time (either houses will become cheap or CPI will catch up).
If you want a simple explanation as to why it is that CPI bounds houses and not the other way around - just look at the recent post-covid deurbanization trend (and the carnage that's going on in San Francisco or New York real estate markets). There's so much land that can be utilised once you understand that you really don't have to be in downtown New York. Then, homebuilding costs are basically CPI.