That doesn't seem quite right. If you're moving up, your decision to buy will primarily be based on affordability, even if the old house had a better interest rate. And in a high-interest environment, house prices become lower and partially offset the extra interest expense, so affordability hasn't changed all that much.
Prop 13 has a big effect but more so in downsizing (eg empty nest / retirement) than in upsizing.
California’s prop 13 was found to have this effect. So too will the prior low mortgage interest rates.