Jira Cloud app for Microsoft Teams has been updated to support Jira Service Desk projects. You can configure by selecting the project, choosing which service desk queue you would like to monitor and pin that as a Microsoft Teams tab.
Please see below on how to configure Jira Service Desk queue in Microsoft Teams
Configure Jira Service Desk queue in Microsoft Teams.
Jira Cloud Connector will be sending out the notifications for Jira Service Desk items as well based on how the connector is configured.
Jira Cloud Messaging Extension will also search through Jira Service Desk items and those can be shared in channels or personal chat in the form of a rich card.