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.

Currently this is unfortunately not possible because check ins to Sentry will only include the information that they need (ie. environment, schedule and status). Moreover, if we open an issue that has been created due to monitor failure (the same goes for missed monitor issues), and we look at its tags section, you will see that the only information there is the monitor's config and status. This is why, when creating these alerts, we give the monitor slug as a matcher example.

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 to them.