It's a normal brake system, uses brake fluid (so hydraulic) with a Bosch brake controller for ABS and stability control - so fly-by-wire hydraulic brakes. For track use, many of us are upgrading the brake fluid to a higher temp one and also swapping brake pads to again be more tolerant of high temps. The stock parts are more about ride quality and low brake dust which isn't very fun on track
Regenerative braking happens via the motor, so the brakes aren't impacted at all by the regen braking (they just work less) but they still function like an ICE car. The regen braking is very similar to being in a low gear in a manual car and lifting off the throttle, the car naturally wants to slow itself down without touching the brakes at all.