Two of these don't need any machine learning; they just needs more information to be encoded in the notifications, and more comprehensive filtering to be built

Two of these don't need any machine learning; they just needs more information to be encoded in the notifications, and more comprehensive filtering to be built into the notification subsystem. Your second and third conditions just require the ability to build contact groups that get higher priority for notifications (and, of course, an indication within the notification of who the sender is). The "urgent" part of the first is obviously somewhat more complicated, but the "from my boss or team" is also just a contact group. I don't use Slack, so I am unfamiliar with its specific capabilities, but if it gave the ability to mark a message as "urgent", that could be transferred through to the notification, and allow additional filtering on it. Alternatively, I suspect that it already allows (for whatever the Slack equivalent of the "server owner" is) for the creation of arbitrary channels; if your team created an "urgent issues" channel, the channel information could easily be encoded into notification metadata to allow filtering on.