Hey Mike,
since I don’t have the Controller here to see what it does, I can only assume things.
Buildbotics manual says “estop” button is software controlled, so I would assume it sends the command to stop the spindle the same way you send it when you click on stop spindle on the screen or when you send the M05 command which would stop the spindle. But it would not be powering down the VFD, this would need to be accomplished by an external safety circuit. And the safety circuit would not power off the VFD, but activate one of the Intelligent Terminals on the VFD which you would have programmed to serve as ISO 13849-1 Safety Inputs, or similarly programmed to initiate the spindle stop command (optionally with brake command).
(Source: Omron MX2 User’s Manual)
(Source: Hitachi WJ200 Instruction Manual)
Btw, using an external safety circuit would also allow to power off a trim router automatically when the Emergency Switch of the (external) Safety Circuit is pressed.