"Too big to fail" is crony capitalism.
I mean I'd argue the "too big to fail bailots" are a particularly ineffective bit of market intervention in the long term, but generally speaking "market intervention to save the health of the economy" is bog-standard neoliberal, capitalist ideology. The only whiff of socialism comes from recognizing that without guardrails the fully freed economy will destabilize, possibly from angry with pitchforks, angry they can't afford food, shelter, and the basics. So—it is still serving the ultimate needs of the capitalists who run society by not ousting them when they do destabilizing things.
Plus, if this weren't capitalism, no society in history would have been capitalist making it a bit of a useless word for sticking to extant political movements.
This is not about a question of ideology. It's about the wealthy being protected and fostered, by any narrative necessary. On sunny days, it's liberalism, on rainy days it's socialism.
Isn't market intervention more like corporate socialism though? I mean that's literally not capitalism.