The Federal debt needs to be rolled over every now and then. At certain interest rates, the costs of servicing the debt become unacceptably high. Where is that 'breaking point'? If you see some serious analysis of this, please let me know.
But there is a higher bound to which the Fed can feasibly raise interest rates. So it is possible that the Fed will be forced to choose between keeping rates low, keep buying Treasuries and destroy the dollar through runaway inflation, or raise interest rates and bankrupt the US government.
The Fed sets a different rate, one that banks use to lend money to each other. It forms kind of a floor for lending. They raise it to reduce lending, and thus slowing down the economy in general (and thus reducing inflation).
They've kept the latter at nearly zero -- arguably for the not-great reason of propping up assets. If anything, raising that would make bonds more attractive relative to stocks, dropping the interest rate further. Instead, we've gotten inflation, but only in the asset markets, not consumer inflation.
They actually wanted consumer inflation to be higher, so that consumers would be forced to put their money in asset markets rather than holding it in cash. They've finally gotten their wish, though it's likely that it is due more to pandemic-related shutdowns than to monetary-based demand.
Short-term treasuries and the fed rate are also directly related. Increase the fed fund rate, and short-term treasury interest rates will have to go up as well to remain competitive.
High interest rates will devastate parts of the economy, but that's a different and more well known problem.