To enable customers to send messages via their preferred mobile app to agents in the Service Console, the "Messaging" feature in Salesforce is recommended. This feature integrates various messaging platforms with the Service Cloud, allowing agents to communicate with customers through their preferred channels, enhancing customer experience and engagement.

Entitlement processes, milestones, milestone actions, and entitlements are features that can be configured to ensure the contracted service level requirements for its clients are being met. Entitlements define the levels of support that customers are eligible to receive based on their products, service contracts, or warranties.
Entitlement processes define the timeline and steps required to deliver support to customers. Milestones define the critical steps in the support process, such as first response time or resolution time, and track whether they are completed on time. Milestone actions define the automated actions that occur when a milestone is approaching, violated, or completed, such as sending email notifications, assigning cases to queues or users, or changing field values. Verified References: Service Cloud Consultant Certification Guide
& Tips, Set Up and Manage Entitlements and Milestones

The Omni-Channel Supervisor tab is a feature that allows managers to see which service representatives have not accepted new cases recently using the Lightning Service Console. It provides real-time data on the status, capacity, workload, and performance of agents and queues. Verified References: : https://help.salesforce.com/s
/articleView?id=sf.omnichannel_supervisor_tab.htm&type=5 : https://help.salesforce.com/s/articleView?
id=sf.omnichannel_supervisor_monitor_agents.htm&type=5