Somehow we went from "the state should be financed from taxes" to "in hard times the state should spend more than it has to quickly get back to the good times where it can pay back its debts" to "the state should spend to stimulate the economy in both good times and bad times, and as long as the economy grows fast enough it doesn't matter that this spending isn't covered by taxes".

This is in effect an infinite-money glitch, until you overplay your hand and a market upset bankrupts the state (or the state triggers hyper-inflation in an attempt to prevent bankruptcy). Austerity is just a roundabout way of saying "let's get more breathing room by abusing this infinite-money glitch less".

In an ideal world any country would go through periods of austerity to get rid of wasteful spending, before increasing spending again. But of course this is not how politics works: it's hard to sell to voters, and the things that get cut in "austerity" are often not the most wasteful things.