To ensure customers can access only their cases, including those created on their behalf, configuring a sharing set in the Experience Cloud site is recommended. This grants site users access to case records associated with their contact, ensuring secure and appropriate visibility in line with the requirement.

Configuring case escalation rules is an approach that can notify support managers when a new case has been untouched for more than two business days. Case escalation rules are tools that allow administrators to define the conditions and actions for escalating cases to higher-level agents or managers. Case escalation rules can help ensure that cases are handled in a timely and efficient manner. Verified References: : https://help.
salesforce.com/s/articleView?id=sf.case_escalation_overview.htm&type=5 : https://help.salesforce.com/s
/articleView?id=sf.case_escalation_create.htm&type=5

Explanation
Omni-Channel Supervisor is a solution that can enable supervisors to respond to flags and provide responses that only the agent can view. Omni-Channel Supervisor is a tool that allows supervisors to monitor and manage the work and performance of agents in real time. Omni-Channel Supervisor can help supervisors respond to flags raised by agents who encounter issues and provide private coaching messages that only the agent can see. Verified References: :
https://help.salesforce.com/s/articleView?id=sf.omnichannel_supervisor_overview.htm&type=5 :
https://help.salesforce.com/s/articleView?id=sf.omnichannel_supervisor_flags.htm&type=5 :
https://help.salesforce.com/s/articleView?id=sf.omnichannel_supervisor_messages.htm&type=5