As a manager you have a responsibility to communicate this to your team and give them resources to deal with the emotions (you, the manager, being one of the resources).

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.

At least they weren't announced as 'useless', so there is that.