To force Sagisō to crack under pressure, that'll depend more on her opponent. Kidomaru was the closest she's been to death, but he wasn't the one with initiative in the situation. He only managed to catch Sagisō after Kin had already left him half dead, and hence it was Sagisō threatening to kill him rather than the other way around, that's why as opposed to fear she displayed anger in response to her injury.
The invasion is another story; the most perilous things Furijia was faced with were the flood, and Taiyo's yelling. The former of which being the only serious threat.
I get that you feel these were extremely dangerous situations, and I agree, but not to the extent to which you describe it. Sagisō's moments of weakness are often as she deals with the aftermath of a battle, not during the thick of it.
Perhaps upping the stakes through displays of weakness would be rather good for all our characters, but the stakes aren't easy to up. Every battle is essentially one where a Shinobi's life is on the line, danger to ones life isn't the most suitable stake given that it will be the only constant stake for every single confrontation. With the same stake being put forth for every confrontation, it's bound to get stale.
However, disregarding that, the last time we had this conversation is particularly the reason why I've dedicated my time to writing more in-depth posts that detail the thoughts and emotions Sagisō feels when she acts. Between the last time I addressed this, and this time, nothing even slightly worthy of mention has occurred event wise to influence Sagisō as external factors. Unless you consider Kiro moving into the Hyuga clan as worthy of mention with regards to influencing Sagisō's character development. However, internally, I'd like to think that between her time with Takato, the drunken song she'd sung, and her thoughts in the analogy of the field, I've added a lot to her 'indifference'.
You're certainly entitled to think otherwise, but I'd respect if you take into account what I've doing to remedy your concerns rather than pulling from the same handful of examples which I've addressed numerous times.