I'm not an economist but this seems wrong
Buying a bond means you are lending money now, in return for more money later. The amount you get later is made up of the price you pay now plus the interest, ie the yield. So if the yield goes up, the price goes down. (You don't have to pay as much for a bond when the yield goes up).
This is categorically not true. If it were then Congress would pass legislation ordering the Fed to buy securities from the Treasury at whatever rate it liked (or abolish the Fed altogether and just directly spend money into existence). Congress in fact wants to provide savings vehicles, it's not actually necessary for Congress to borrow to fund the federal government. Sure it's necessary under current law but Congress by definition can change that law. That it chooses not to is an expression of a preference.
Or is it simply about interest rates, I guess, since higher interest rates cool the market and lower interest rates warm the market. So investors are thinking a recession is coming and the Fed will need to lower interest rates to stimulate.
But, in a recession, the stock market tends to nose dive, which prompts a lot of people to flee to fixed-income securities because they're viewed as being safer. Which would also drive down yields.
Not always:
https://en.m.wikipedia.org/wiki/United_States_federal_govern...
"Market consequences ... U.S. treasury bonds, which had been the subject of the downgrade, actually rose in price and the dollar gained in value against the Euro and the British pound, indicating a general flight to safe assets amid concerns about a European debt crisis.[31]"
Basically, no one believes rating agencies with respect to the US paying its debts - but they do believe that if the US government is in chaos, it will be bad for the world economy.
One should also remember that US bonds are denominated in US dollars, which the US government can print. Also, if you're comparing to "cash" you probably mean "US dollars" which are backed by the "full faith and credit" of...the US government.
Bond prices go down when interest rates go up. As such, an investor who thinks that interest rates will go _up_ will reallocate from long-term bonds to short-term bonds, rather than the opposite as you stated.
More generally, a yield curve inversion is when the interest rate you earn on short-term debt ends up higher than that of long-term debt of the same quality.
I don't think the issue is that the inversion causes the recession. It's more an indicator of pessimism in the market. It implies that investors think that interest rates are going to get worse, so they look to buy more longer-term bonds in order to try and lock in current yields for a longer period of time. That increases demand for those assets, which drives down their price^H^H^H^H^H yields.