How to Achieve your requirements:
Connection Ownership Is User-Specific: Each connection (Outlook, SharePoint) in Power Automate or Copilot Studio is tied to a specific user’s credentials. When you share an agent or flow, it continues to use the original creator’s connections unless each user authenticates their own. Please keep it in mind.
Sharing with Run-Only Permissions: Power Automate supports sharing flows with run-only permissions, allowing other users to run the flow using their own connections. However, this requires configuring the flow’s connection references to allow each user to authenticate their own connections. It's little bit of tedious.
Use Connection References and Run-Only Users: In Power Automate, define connection references for Outlook and SharePoint connectors.
Share the flow as run-only with users or groups. Each user must authenticate their own connections when they run the flow, so the trigger and actions run in their context.
Triggering on Each User’s Mailbox: The trigger “When a new email arrives” must be configured per user’s mailbox. For shared flows, users need to have the flow enabled with their own connection authenticated. Alternatively, consider using a shared mailbox if you want a single trigger for multiple users.
Agent Deployment Strategy: You can share the agent as a template or solution so each user can import and authenticate their own connections. Or use environment-level permissions and connection references to allow multi-user access with individual authentication.
Limitations: There is no out-of-the-box way for a single shared agent to automatically trigger on multiple users’ mailboxes without each user authenticating their own connection. Using service principals or application permissions can centralize access but requires admin setup and is more complex.
