I've said this before and linked the relevant laws, but I'm too tired/stressed to provide links etc. so I'm just going to say it. UK laws are different, I'm not knowledgeable on those laws, but in the US the laws vary by state, and many states have "mental health acts" that don't fall under the same regulations that criminal laws do. People committing/accused of committing a crime always have certain rights, but that doesn't apply whatsoever here, because no one is committing/accused of committing a crime.
Instead, a police officer is allowed to interpret very vague "mental health" statutes however they like, so what happens to you is completely dependent on the officer assigned to you. In the US where we have a systemic problem with police who are already willing to violate people's rights when they can get away with it, this sets up a very dangerous situation.
I've brought this up before regarding the blanket statements like this is "nothing to stress about"; for people that have already interacted with reasonable officers that's true, and they can already surmise that based on their previous interaction. But if you live somewhere with hostile law enforcement and have already been threatened, had your rights violated and other things I can't talk about on here, then this is absolutely something to worry about.
I'm hesitant to say even the small amount I've said on SS, and I imagine that anyone else who also faced hostile law enforcement is similarly hesitant to speak. So the narrative becomes 100% that reasonable, non-aggressive cops are just talking to people, and then that gets repeated with others saying things like it's nothing to worry about, they won't do anything, etc. This isn't reality though, and as glad and relieved as I am for all the people who had safe interactions, I don't want that to be 100% of the narrative when that's not reflective of reality.