For USD, the sole rights to create new US Dollars are given to Federal Reserve. Fed has the monopoly over creating USD or printing this money.

This is absolutely incorrect and untrue. Once again, a lack of understanding how the money supply works.

It is true the Fed has the ability to print banknotes. That is the only Fed liability that is legal tender ie USD. Reserves are not legal tender. Instead they are a financial product that can only be held by depository institutions and is pegged to the USD. It is basically a token.

As you pointed out, physical currency makes up only a fraction of the money supply. Most of the currency is in digital form.

So where does that come from?

Under fractional reserve banking, which the USD, EURO, Pound, and YEN all use, the money supply is expanded by commerical banks creating money out of thin air by issuing loans.

So to state the Fed has the sole rights to create USD is untrue. Other than the few banknotes created, the commercial banks have the rights to create USD.