When you message somebody whose notifications are paused, the note under your message now has Notify anyway. It sends that one message through, once a day for each person, and only in a direct message to one person. Press it a second time the same day and it says you already notified them. A conversation they muted stays muted.
A live Link has Copy link, on its card and at the foot of the sidebar. Whoever opens that address lands in the conversation and is told a Link is live there, with Join to press. It never joins by itself, and it opens nothing for somebody who could not already see the conversation.
Set a status has Pause notifications until it clears, for a status that starts now and clears within a week.