The Fed is a creature of Congress, which is to say that Congress completely controls the Fed. All talk of the Fed's independence has no constitutional basis. The Fed was created by an act of Congress and can be restructured, abolished, or otherwise changed however Congress likes by subsequent acts of Congress. Indeed, in the history of US central banking, Congress has done so before. Therefore, the Fed's continued existence is predicated on not motivating a congressional majority plus the executive or alternatively a veto-proof congressional majority to change things. Practically and observably speaking, that means when Congress says "print" the Fed says "brrrrrrrrrrrrrrrrrrrrrrrrr." There is no operational limit on how much money Congress can spend. There are real limits though, in particular the productive capacity of the economic zone that does business in US dollars. If, for example, China were to withdraw from the dollar denominated global market, it would be a severe supply shock and result in massive inflation.

Furthermore, most money in the USA isn't even reserves, but rather bank deposits. Theoretically bank deposits are supposedly somehow constrained by reserves, but that hasn't really been true for well over a decade. Raising rates doesn't directly impair banks ability to originate as many new loans and corresponding deposits as they care to. Conceivably, higher rates could reduce the demand for loans from credit-worthy borrowers, or even reduce the pool of credit-worthy borrowers directly, but I'm not sure it doesn't end up being a wash after accounting for inflation.

Personally I suspect most of the effects that we do see are related to hysteresis rather than a fundamental transmission mechanism from interest rates. That is to say, the shocking effects we see from rate increases aren't due to a fundamental change, but rather a lag while market participants to catch up with the new rules of the game.

Another important factor is the prestige media using all of its persuasive powers to convince market participants that Fed actions will result in a downturn. There certainly is a large psychological component to economic activity.