The P/E ratio references "price" and "earnings". Both "price" and "earnings" are denominated using money. So it's not obvious to me how an increase in the money supply should affect this ratio.

BTW, in Shiller's book which was published right as the dot-com bubble popped, he has a chapter listing out similar late 90s structural factors, many of which could lead to permanently higher stock prices in theory.

Nasdaq is about 8x higher now than then, so 4x higher M2 is tight. Ofc there is always a chance that this time is different and that the markets are genuinely much more efficient :-)