"What happens next is that they buy and sell government bonds in the open market."
This describes how central banks operated in the U.S. before 2008 and in Canada before the 1990s. The Federal Reserve and the Bank of Canada both set a target for the overnight interest rate, and then they hit that target by doing open market purchases (or sales) of bonds, effectively adding funds to (or draining funds away from) the overnight lending market. By changing the quantity of funds, they influenced the interest rate.
What changed is that both central banks introduced interest payments on balances that banks hold at the central bank. Previously, these balances earned 0%. With this new tool, they could directly set the overnight interest rate by adjusting the rate paid on these reserves, eliminating the need for regular open market operations.
You make it sounds like they aren't doing regular open market operations, but as I understand it... they still do?
https://www.newyorkfed.org/markets/domestic-market-operation...
The Fed still does purchases and sales, but not for the purpose of driving the overnight interest rates towards its target. The level of the overnight rate is not affected of any purchases or sales that the Fed does.
If the Fed makes or receives a loan at specific interest rates (even if only overnight), that's pretty much economicaly equivalent to buying or selling bonds.