If you set Slack to do-not-disturb, people sending a direct message to you will be warned that you won't be notified and might not see it -- but will be given a

If you set Slack to do-not-disturb, people sending a direct message to you will be warned that you won't be notified and might not see it -- but will be given an option to "punch through" the do-not-disturb setting for important, interruption-worthy messages. That seems to largely achieve what you describe.