Since 15:53 UTC, every down alert and every reminder carries an Acknowledge link: a button in email, an inline button in Telegram, a link in Slack, Discord, Teams, Google Chat and ntfy, and ack_url in webhooks. It is valid for 7 days and opens a page with one button. Acknowledging puts the incident on hold, as the Incidents page's button (now called Acknowledge) does: reminders stop, the sidebar mutes it, monitoring and the recovery alert carry on. Who acknowledged, member or channel, is shown in Incidents and in the activity log, and the API's incidents carry acknowledged_at and acknowledged_by.
A channel now has the option Only if nobody has acknowledged it. With a delay set, the channel gets the down alert only when the outage has run past the delay with no acknowledgement. Slack at once, the on-call SMS after 15 minutes if nobody picked it up: that is escalation.
And a monitor can have its own Alert delay: right away, or if still down after 2 to 60 minutes, in the form, bulk edit and the API (alert_delay). The incident is still recorded from the confirmation; only the alerts wait, and the longer of the monitor's and the channel's delay counts.
Details in Alert rules.