No, no it's not. USD denominated interest rates are whatever the Fed wants them to be. The Fed controls the entire USD yield curve, although that control does weaken a little as maturity goes out into the future, but not more than about 10%.
Treasury auctions are kabuki theater[1]. Thanks to the Primary Dealer system it's impossible for an auction to fail. While the nominal rate may bounce around a few basis points, at the end of the day the Fed absolutely controls rates. They will literally create reserves and lend them to primary dealers at whatever rate is necessary to assure Treasury sells as many securities as it needs to at something near the target rate.
Typically when weaker countries do this, it was once considered a sign of fundamental weakness and a sure sign that a currency crisis was imminent. The US abandoned the same principles in government finance that it once advanced through institutions like the IMF. It's not that it was bad advice; we see the results of the irresponsibility in today's markets. The US is just a big bad 'basket case' without much in the way of financial credibility past what it can dictate through market manipulation.
Makes you wonder if there could be a scenario where the Fed raises rates for interbank lending and for loans to the general public but maintains a near zero percent interest rate on its own debts. As far I can tell the Fed operates with impunity and can do whatever it wants. So why not stave off inflation while protecting itself at the same time.
Not if they do YCC. Yield curve control. Which they are sort of doing at the tail end of the yield curve. And they did that back in the 40s as well when US had tons of debt from all the spending in the war.
