How do I use the eGPU to power MacBook's internal screen
I'm pretty sure they're not designed to accelerate your internal screen, only external, plugged into the eGPU itself.

From the Sonnet eGPU Manual


  
  Set up your monitor(s);
  To obtain the best graphics acceleration for applications like games, set a display connected to the eGPU as
  the main monitor. Open System Preferences:Displays, select Arrangement
  and drag the white menu bar to the external monitor. Drag the monitors
  to mimic the physical arrangement. If you want to tile your displays
  into one large space, Open System Preferences: Mission Control.
  Uncheck Displays have separate Spaces.
  Note that if you mirror an internal and external display together, internal graphics will be used.