If you don't know if they're working, don't fucking slack them. How about you check their calendar or send an email.
Slack is not for asynchronous communication.
It's amazing how high and mighty people can be and then they ping people for non-emergencies while they're on vacation.
Depends on the organisation.
Where I'm currently working, we use Discord. Discord is similar to Slack.
It is explicitly for asynchronous communication. We are supposed to not expect immediate replies to questions and comments on Discord, especially as other teammates are in different timezones. Sometimes there's real time chat, but it depends who is on at the time.
I posted some comments yesterday. There was one reply within a few hours, and two more this morning.
Email is pretty much deprecated. Nobody uses it, except to set up calendar entries for meetings, and formal things like HR and invoices.
Sick/vacation days are harder because we pay for whatever I get an invoice for. Since we don’t track what people do on a day by day basis (I often don’t even know if someone is working that day until I reach out to them or slack, or vice versa), there’s nothing stopping them for billing me for extra hours. And to be honest I really wouldn’t care. I just care about output and quality of that output.