Well, what you seem to be describing is M2, aka actual money available for spending. Which is a rather large factor in the general price level.
Think about it this way: How can M2 increase without M0 also increasing? Then we can look at those mechanisms and determine if they are to "blame" for the recent price increases. I think they are not.
It is quite simple. There are no reserve requirements anymore.
For every $1 in notes and coins, there are about $30 in bank deposits that exist as a number on a spreadsheet somewhere. So instead of actually printing more, when the central bank "prints money" it means they edit the number in their spreadsheet, increasing their own bank balance. Then they spend that balance buying things like government bonds and treasury bills (which also exist only on spreadsheets)