For any business process that needs to run at a specific time interval (in this case, "once a week"), a Scheduled flow is the standard tool. A scheduled flow allows the Platform Administrator to define a frequency (Daily, Weekly, or Once) and a start time. The flow can then query all relevant Account records and perform the logic of counting open cases and updating the parent record autonomously. Record-triggered flows (Option B) are inappropriate here because the count needs to happen on a schedule rather than being triggered by an individual record edit.
Autolaunched flows (Option C) must be called by another process, such as a button or Apex, and do not have their own timing mechanism. "Automation event triggered flow" (Option D) is not a standard type of flow used for recurring batch processing