Yes the control of money is through the Federal reserve of the US, for the US there is no central bank that it gets money from. I fear you may be misinfor.ed about how is banking operates.
There is no international central bank that the US fed falls under. It is arguably the internal banking leader though as the us is currently the sole world power. Euro holders central bank is the ecb. Bank of Japan, bank of England, and Russia and China have their own central banks but tlwhile they work together often they are seperated. The concept you have that the bank of international settlements is the sole central bank for the world is simply wrong and it's exceptionally wrong.
Yes political parties in the us control the money supply because the fed chairman does the bidding of the POTUS despite the national media nonsense that the fed is independent. It is not, I suggest reading this short article if you are actually interested in learning how various presidents actually control the fed.
The standard reply of the Fed and its partisans is that any such measures, however marginal, would encroach on the Fed's independence from politics.
mises.org
If you aren't interested in that her is a video you can put on and listen to.
Here is a movie that goes over it
So back to the topic yeah the political elites do control the money. They control it through the US dept of Treasury and the very real influence the POTUS has on the fed board and fed chairman. If a president is anti inflationary like Dwight then the fed policy will be anti inflationary, Dwight and Reagan telling Volker to raise interest rates are examples. If they want to generate spending the fed will let the spigot flow see Clinton, bush,Obama trump and Biden and trump again. You can actually go further back and the rothbard radio discussion I posted does so citing names of administration officials and dates explicitly.
In central banking fiat societies yes banking is and inflationis under the control of the government.
So that alone should tell you Walmart doesn't control the currency it doesn't control inflation, it can only operate in the currency market it is in, and the Minny Fed and NBER and general knowledge of how Walmart handles their vendors confirms Walmart isn't the reason your prices are going up and that their actions for us citizens have been anti inflationary