Buffy seems to act more like a boundary guard in a (civil?) war than a vigilante. A bilaterally acknowledged war, even Anya says Buffy's just doing her job. Spike is stakeable when he's perceived as an active threat. Chipped Spike is not stakeable. Warren who is a threat is not stakeable but Warren's a soldier in a different war, human person on human person not demon person on human people.

Buffy stakes newly risen vampires all the time, often before they make any threatening move.
Staking them before they rise up and attack her is vanishingly rare. I can think of two, the one she hears growling while still underground at the beginning of OOMM and the one who declares herself not peaceful in the funeral home opener to Help. Partly it's a consequence of the decision to use game face to show "I want to eat you" aggression and thus avoid imagery of human people with human faces being stabbed to death by our hero. Nevertheless they do avoid and in show explanations have to look elsewhere. As a biologist I rather like the realpolitik elsewhere that the strategy of letting those who run in terror run allows the slayer's fearsome reputation to be spread by them.

I really don't think Spike believed her.
Then I have issues with him clinging to his own preconceptions in the face of her outright declaration. Like Riley! The poor guy can't win :)