When a government that directly control their central bank spends money, they have their central bank create it out of nothing. When they tax, the money they collect gets destroyed again. It's not useful to think of them as a household budget with "a certain amount of trillions", because not a single household can create its own money supply, force others to use it, or tax it back.
While it's absolutely true that such governments cannot create an infinite supply of money without massive causing inflation, nor get rid of taxes at will without causing inflation (hi Liz Truss), it's much less simple than "bigger money supply = more inflation" (as the past couple of years have shown). The current inflation is not driven by too big a supply of money causing massive spikes in consumer demand, but by high energy prices (Russian/Ukraine war) and still not fully recovered supply chains and production after covid.
Furthermore raising interest rates is what is more likely to trigger a recession than not: it will make more people default on their mortgages and unable to pay other bills, which will have a domino effect on other spending and businesses. Inflation has that effect as well, but central banks cannot fight this kind of inflation in a meaningful way by raising interest rates. It's not going to stop Putin, reduce energy prices (although I'll grant you that kicking people out of their houses and business shutting down will reduce demand for electricity and gas on those premises), or fix supply chain problems.
A more in-depth explanation: https://www.taxresearch.org.uk...