I set a team as a tag in my monitor config, and I would like to ping this team through Slack alerts using this tag.

This is currently not possible because check-ins to Sentry will only include the information that they need (ie., environment, schedule and status).

The closest workaround to this would be to create an alert rule for each one of your monitors. Since you know that each monitor has its own assigned team, you can mention (@) that team in the notes part of the Slack alert config. Alternatively, you can have a different Slack channel where each team will only see alerts associated with them.