Would you help me understand the design of this induction motor?
Based on the video, I believe that you are correct. This is a permanent split capacitor motor. The capacitor is connected in series with the auxiliary winding to provide a phase shift to the current in that winding so that the motor has a defined direction of rotation and will start automatically. The best way to identify the auxiliary winding is to observe its series connection with the capacitor. It may also have slightly smaller wire. There are four main coils and for auxiliary coils in a 4-pole motor.