If a mortgage payment is $1800 of interest and $700 of principal at 7%, a buyer is in the same position if rates go down to 3% and the payment is $1400 in interest and $1100 of principal (numbers are made up, I don’t have time to calculate the exact values). In the 2nd case, the home price would be higher and the lower rate would mean reduced financing costs, with the same TCO in the end.
Bonds work the same way, as the yield goes up above what the bond was issued at, the face value of the bond decreases, only the housing market has limited supply so prices didn’t go down when rates went up.
If yields go down, the face value of the bond goes up, just like with houses.
The only thing that will lower housing values is more supply.