To address the issue of high-priority cases exceeding service deadlines, configuring Secondary Routing Priority in Omni-Channel is recommended. This setting allows prioritization of high-priority work items, ensuring they are routed and addressed by agents promptly, in alignment with SLA commitments.

Email-to-Case is a solution that can meet the requirement of Universal Containers' email policy that requires all email traffic to remain within its firewall. Email-to-Case allows administrators to set up an email service that runs on their own servers and converts email messages into cases in Salesforce. Email-to-Case does not require any email messages to be sent or received outside the company's firewall, unlike On-Demand Email- to-Case. Verified References: : https://help.salesforce.com/s/articleView?id=sf.case_email_overview.
htm&type=5 : https://help.salesforce.com/s/articleView?id=sf.case_email_email2case.htm&type=5

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.