It can issue as many dollars as it wants at will. There is nothing to stop it except the destruction of the global economy if it becomes too reckless. See Zimbabwe Hyperinflation to see what happens when the central bank becomes unhinged. My friend still has a 100 trillion dollar note on his fridge from that period.
Prior to May 2020, M1 included currency in circulation, demand deposits at commercial banks, and other checkable deposits.
After May 2020, the definition was expanded to include other liquid deposits, including savings accounts. This change was accompanied by a sharp spike in the reported value of the M1 money supply."
A lot of the former is older people on public health care passing it on to people who already had homes, so likely joined the landlord class with the inheritance or sold it to people looking to rent it out. The latter's homes (if they had them) were sold to investment firms to pay the medical bills.
Most of the dead weren't buyers, and the supply that went on the market wasn't enough to change things.
I hate to be conspiratorial but there are times when I think this market is so irrational that there is some kind of larger force at play. It's not like the pandemic created more demand for homes -- if anything (and I hate to be morbid about this) there should be fewer buyers in the market and yet everything continues too tick up. And on top of that the rental market is completely irrational as well.
It's really hard not to give in to the idea that the market for housing isn't being manipulated by larger forces.