The last time the debt limit was raised on December 16, 2021, what happened:
The US Treasury took $0.64 trillion on the market in 6 weeks, of which $0.28 trillion (44%) were bonds, the rest were short–term bills, deposited $700 billion to the Federal Reserve account (in January the budget surplus).
The Fed’s reverse repos did not change much last time, remaining in the region of $1.6-1.65 trillion, everything went into reducing the cache of US banks of $ 450-500 billion.
The UST10Y yield rose from ~1.4% to 1.8% by the end of January and to 2% by mid-February, but then the Fed was entering a policy tightening cycle. In the first two weeks, the S&P 500 rewrote the highs above 4.8K, after which it confidently turned down;
The situation then was different from the current one: the Fed was still conducting QE and bought ~ $120 billion worth of securities in 6 weeks, now QT in similar volumes (the supply of government debt to the market will be greater). Back then, the market was already laying the beginning of a rate hike cycle, now the cycle is on the wane and the market is laying a decline. Then the banks had a large amount of free liquidity, now it is comparable to what Yellen would like to take to her accounts and she will have to fight for it, which implies pressure on government bonds (premiums for loans).