Post dotcom bust and 9/11 interest rates were dropped significantly to spur consumer spending.
The majority of people base their housing budget on the monthly payment they can afford.
When interest rates are low, people can afford higher principal values.
When interest rates go up, the amount of a monthly budget that can go toward principal goes down.
Housing prices will tend to fluctuate to match what people can afford, and what people can afford is determined by their monthly payment.
When you’re bidding against other buyers, the more they can borrow for a constant monthly payment, the higher the equilibrium price will be.