Doesn't the Fed control long-term interest rates, and hasn't printing trillions of dollars driven the housing market up?

The Fed controls short-term rates. Bond investors set the long-term rate on your mortgage. And yes, the money-supply surge helped fuel the housing run-up. The Fed's only direct lever on long rates is buying Treasuries and mortgage-backed securities in the open market, which it did at large scale during the pandemic. Outside of that, long mortgage rates are set by investors pricing the real return they need above expected inflation. When inflation expectations recede, long rates tend to fall without any Fed announcement, and they rise when inflation fears build. On the printing question: a large expansion of the money supply absolutely contributed to the housing run-up. It was the ammunition. But long-run inflation depends on two variables, how much money is created and how fast it changes hands, which economists call velocity. Velocity spiked when people came out of lockdowns spending freely, then normalized, and it had already been trending down for two decades alongside an aging population. That is a big part of why a huge money-supply increase never turned into runaway hyperinflation. The money-supply number alone never tells the whole story; velocity decides how much of it shows up in prices.