No offense, but when a coworker dies
it’s not about you.
When a coworker died at work we usually understood the family was the one that needed support, not us. And if the family asked for privacy, then they got it.
And if any of us needed support, we helped each other. We didn’t need HR to pencil in a meeting.
And no, when someone dies their cause of death is not automatically public and most people (including employers) respect that.