To track specific stages of a support process and measure the time elapsed within those stages, Salesforce provides Entitlements and Milestones. Milestones represent required steps in a support process, such as "First Response Time" or "Resolution Time". When combined with Business Hours, Milestones allow the system to accurately calculate how long a case has been in a particular status or assigned to a specific team, excluding weekends or non-working hours. This provides leadership with granular reporting on "Team Performance" and SLA compliance.
Escalation Rules (Option A) and Assignment Rules (Option C) are primarily routing tools; they can move a case but do not natively provide the timestamp-based tracking and reporting necessary to see duration across multiple "handoffs". Record-Triggered Flows (Option B) could theoretically be used to stamp fields, but this would require significant custom development and would not offer the native, out-of-the-box reporting dashboards that come with the Milestones feature. Therefore, Entitlement Management is the standard solution for tracking time-based service metrics.