Easiest way would probably be a custom field (either a simple single select list with your team names or a group picker if you create groups for your teams).
You can then use quickfilters on your board to filter the issues (if you click on the team's quick filter you will only see the issues assigned to that team (using the custom field)) deselect the filter and you'll see all tasks again.
...PermissionsStartOnly=true User=www-data Group=www-data ExecStart=/opt/jira/bin/startup.sh ExecStop=/opt/jira/bin/shutdown.sh TimeoutStartSec=120 TimeoutStopSec=600 PrivateTmp=true [Install] WantedBy...
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