> Why would money printing increase housing prices but not wages?
Because most of the freshly printed money wasn't immediately used to increase the demand for consumer goods. Instead, it only kept consumer goods demand about neutral, until the summer of 2022.
Without inflation in consumer goods, most businesses don't have increased profits, and no incentive to try to hire more people, which kept wages down.
Instead, the extra money found it's way into assets, pumping up the stock market and housing market.
That started changing in 2022, as inflation hit (which SHOULD have surprised nobody). But the inflation was kept in check by increasing the interest rate.
The increase in the interest rate stopped the amount of money from continuing to grow and even fall slightly. But not nearly enough to reach pre-covid levels.
That means that there is still a lot of excess money in the system slushing around. As long as the real interest rate on bank deposits is still low, people are not tempted to keep them as deposits. So the money stays in assets, maintaining the high price.
> Why would money printing postpone its effect on prices until after interest rates increased?
I'm assuming you mean consumer prices here, not housing prices. Consumer prices stayed low during the pandemic, since people generally reduced their consumption, especially the consumption of services (restaurants, entertainment, etc). A lot of "regular" people paid down credit card debt or increased the size of their savings account.
In 2022, that changed. "Regular people" started to spend more of their savings again, and this caused inflation to rise. As inflation was going up, the fed (and other central banks) slowly increased the interest rate, but not quickly enough to stop the sharp rise in aggregate demand. (And war in Ukraine and continued lockdown in China didn't help either, nor did various initiatives to re-shore production of anything from microchips to ventilators, or for that matter the huge investments of capital currently going into AI infrastructure).
And as demand pushed inflation up, that lead to some increase in the demand for labor. So even if the salaries haven't kept up with inflation, inflation definitely has been increased by the increase in salaries.
Naively, one might expect that the inflationary pressure will cease once aggregate inflation reaches 25% relative to 2020.
And if you wonder why wages haven't kept up. I think this can be explained by a weakening of the demand side of consumer goods, driven by various inefficiencies in how capital allocation, due to the cost of building new and robust supply chains, due to the situation in Ukraine/Russia and China and AI investments etc (as listed above, too).
Why would money printing postpone its effect on prices until after interest rates increased?