I see Greek 10Y debt yielding only +86bps spread over US 10Y debt.
Greek debt to GDP runs above 190% and was not decreasing even prior to the pandemic response. Moreover, Greece has gone through severe debt crisis in the recent past.
Why is the market demanding only a modest premium over US Treasuries?
There is a lot of misunderstanding and contradiction in your question.
If you are concerned that the yield for Greek government bonds is too low, you cannot simultaneously be concerned that there exist high and low interest rates at the same time in the EU. Either Greece pays a premium, in which case you will see differences in yield, or they don't, in which case your question why the spread is so low makes no sense.
The interest rate that a central bank influences is short term. In the U.S., the so called FED Funds Rate is overnight. It is not only influenced by increasing money supply. In reality, monetary policy is a lot more nuanced and the Fed funds market is an inter-bank market. You can read some details at the St. Louis Fed website. Details are not important here though.
In fact, money supply is not really the driver of monetary policy and the monetary base itself has very little impact on total money supply, which you can for example see in the figures provided in this answer.
If a central bank reduces interest rates, usually the entire curve shifts down, although longer tenors are less influenced by short term interest rates. Longer term rates are more influenced by economic growth as well as inflation expectations and probabilities of default of an entity.
Either way, Greece pays a premium, which is most definitely less than it would be if the central bank would not intervene. For example, the ECB announced that it may still buy Greek government bonds until the end of 2024 despite the winding down of the Pandemic Emergency Purchase Program (PEPP). This reduces the risk of sharply higher sovereign borrowing costs.
