Branchial Cleft Cyst — Lateral Neck Mass Anterior to SCM

A 24-year-old woman presents with a smooth, soft, fluctuant mass in the left lateral neck anterior to the sternocleidomastoid muscle at the junction of the upper and middle thirds (marked **A** in the diagram). She reports the mass has been present for 2 years but enlarged rapidly over the past week following an upper respiratory tract infection. On examination, the mass is non-tender, compressible, and transilluminates. Which of the following best describes the embryological origin and internal drainage of this lesion?