I've seen stereotypes of steely resolve and such bullshit

I'm willing to bet that stems from a misreading of a panic response that seems to be more common in women. Everything points to a much higher proportion of women's response to a critical situation is to first just straight up freeze for a few moments, then make the same poorly thought out panic choice someone else might have made immediately, just in a less timely fashion.

It'd be easy to interpret that first part as taking time to calculate a response, if you just ignore the outcomes of the second part being worse not better.

Just look at all the shootings by female cops, waaay too many of them start with them standing around doing nothing whilst their male partner reacts first, then they pull their gun because things got out of hand whilst they did nothing to help the non-lethal response stick, and in the panic turn to lethal force. Or in one tragicomic version, stand around doing nothing, finally decide to take non-lethal action, but panic and accidentally draw and shoot her firearm instead.