Although I’m quite sure there will be disagreement with my post, the Fed does not inject money inject into the economy. Money is created by banks.
The Fed is buying and selling US Treasury bills. Money is not created when it buys, nor is it removed when it sells or allow to mature. When a treasury bond matures, the US Treasury sells a new one to replace it because it doesn’t redeem. If the Fed doesn’t buy it someone else will.
QE results in money creation. When the Fed buys longer term securities (e.g. bonds), they give the seller $ (digital bits but still money) which the seller of the security can use to lend/invest in other parts of the economy.
Without QE operations, you are correct - the fed does not directly inject money, the banks do via the reserve rate and our fractional reserve system.
To the OP - when a bank gets $ from a depositor, it is a liability of the bank. When they turn around and lend that $ to another person, it is an asset of the bank. That 2nd person can then take that money (loaned to them) to another bank, and then it in turn can be loaned again and again... Now, the bank needs to keep *some* of that money to be able to handle requests from depositors (i.e. they want some of their deposits back). They try to manage that by tying up some of the money in the form of CD's (e.g. instruments that the depositors can't just "demand" (demand deposits). How much the bank needs to keep in reserve is complicated, but also controlled via a rate that the federal reserve sets - the reserve rate (aka reserve requirements). The Fed reduced that rate to 0% in March of 2020.
Some banks may have more in reserve than necessary, some less than what they need. If a bank has more than it needs at the end of the day, it might lend it to another bank. Since it is a loan, and they don't do this just because they are nice, they charge the other bank interest. This interest rate is known as the Federal Funds rate, and the federal reserve "targets" and measures a range it would like to see in terms of these loans.
Finally, some banks with excess reserves like to keep those excess reserves with the Fed. The Fed can pay those banks interest on those excess reserves - this is the Interest Rate on Excess Reserves (IOER). The fed can influence bank lending by adjusting that rate. The lower the rate, the more likely the bank will lend out those excess reserves (stimulating money growth via fractional reserve system), the higher the rate the more likely the bank will just part the excess funds with the Fed.
The above is simplified, and if I've missed things - I hope others will point it out and also be kind to me.
Also, I'm now an old geezer, and I learned this long ago (BS Economics magna cum laude '78).