This isn't about the curiosity of collegues??
Again, this isn't some random suicide, these are people in a known high pressure environment already aware this person committed suicide.
The organization can pretend nothing happened (even though everyone already knew), or they can take charge and try and help these people cope with that devastating news and help anyone who might already be in a bad place...
Once you're dead you're dead, that's why causes of death aren't personal... there's no person left.
The organization doesn't even have to frame it in of terms this person's death, just a simple call out that "if anyone is struggling with this loss or needs help come to us".
Anything is better than pretending it didn't happen.