Say enough for work to respond. You do not have to tell the whole story.
A short message can explain the situation, the immediate practical need and who should receive urgent work questions while you are away.
Tell work what happened in broad terms, what you need now, when you expect to update them, and whether you want details kept private.
A very short message
“A close family member died today. I need to step away from work while we make arrangements. I will update you by [day] about what I can manage next.”
If you want privacy
“I am grateful for people’s kindness. I would prefer not to discuss the circumstances in detail, but I will let you know if there is anything practical I need from the team.”
If you need flexibility rather than full leave
“I expect to be handling calls and arrangements over the next few days. Could we agree on the two or three things that genuinely cannot wait and move the rest?”
Make one handoff
If possible, name one person who can redirect routine questions. Repeating the same explanation to many coworkers can become another task.