Case Milestones, a core component of Salesforce Entitlement Management, are specifically designed to track time-dependent steps within a support process. They allow an administrator to define service level agreements (SLAs) for different stages of a case's lifecycle, such as time for first response or time with a specific support tier. Milestones can be configured to start, pause, and complete based on case criteria (e.g., change in Owner or Status). They operate in conjunction with Business Hours to ensure time is tracked accurately against the support team's working hours. This provides the exact functionality required to monitor and report on how long a case "sits" with different teams.

A. Escalation Rules with Business Hours: These rules automatically perform an action (e.g., reassign, notify) when a case remains unresolved for a specified time, but they do not track or report on time spent in various stages.

B. Record-Triggered Flows with Business Hours: While a complex custom solution using flows and custom fields could be built, it is not the standard, out-of-the-box tool designed for this specific business requirement. Milestones provide this declaratively.

C. Case Assignment Rules with Business Hours: These rules are used to automatically route incoming cases to the appropriate user or queue at the moment of creation; they do not track the duration a case spends there.

1. Salesforce Help, "Milestones": "Milestones are required, time-dependent steps in your support process. They’re metrics that represent service levels to provide to your customers. Examples of milestones include First Response and Resolution Times for cases." This document establishes Milestones as the primary tool for time-based service level tracking.

2. Salesforce Help, "Set Up Milestones": "You can add milestones to entitlement processes to specify the time-dependent steps that your support team must complete for cases... Milestones have start, warning, and violation times, and can be set to recur." This confirms their ability to track time intervals for specific steps.

3. Salesforce Help, "Considerations for Milestones": "Milestone timers calculate time based on the business hours specified on the case’s milestone." This directly links Milestones to Business Hours for accurate time tracking, as required by the question.

4. Salesforce Help, "Escalation Rules": "Escalation rules automatically escalate cases when the case meets the criteria defined in the rule entry." This source clarifies that the primary purpose of escalation rules is to trigger an action, not to provide granular time-in-stage reporting.