What you are seeing is the old bills being replaced by the new. Currency is an almost insignificant fraction of the money supply. The bulk is in savings or checking entries, or Treasury debt.
When the Fed ‘adds money’ to the banking system it does so by purchasing Treasuries, the result being an electronic entry on some bank’s account book. The Fed creates the cash to purchase the Treasuries - what it is doing is changing the form of money in the financial system from Treasury paper to cash. The size of the money supply is determined by Congress when it sets the limit on Treasury debt, although as cash it can expand greatly in the banking system due to fractional reserve lending. In theory the Fed could purchase all of the national debt, converting it to cash.
If so, how and what %?