Managers are people too and will have their own emotions they are dealing with.
So sure, you have your own stuff to deal with - use the resources you have for that (eg your manager) but when it comes time to face your team, be a professional and don’t shut down in front of them. They need you too.
Source: I’ve been in management positions and had to deal with a bunch of layoffs and yes, the occasional outright actual death.
"Passed out" is just a verbal typo for "passed on", an accepted euphemism in English for someone dying. I think that slip is forgivable, clearly not ideal, but human beings make mistakes. I also agree with the parent comment that it isn't management's place to provide details about the death, but IMHO they have a responsibility to say that's what happened.