I think that we need a pinned page that has everything we know (we kind of have one but it isn't maintained to my knowledge) AND everything we don't know, both with URLs showing where we got the information. Right now the list of things we don't know is quite long, including this one.
What does this mean? (I'm not a towing person, I don't know the terms.)
The brake assist is in the wiring, and just relays the vehicle's brake signal to the trailer. So as long as you have the trailer wire harness hooked up properly it should work fine (any vehicle). If the question is really about something in software and hardware (i.e., more elaborate than simply conveying the brake signal), then maybe @Crissa's answer is the right one.
A brake controller is required for (most) trailer brakes. "Any vehicle" with just wiring/relays will not activate the trailer brakes on most trailers. The wiring/relays alone, will activate the brakes lights and turn signals, but a brake controller is required to activate the actual brakes on most trailers. The brake controller activates the brakes and uses sensors to determine how hard you are braking and activates the trailer brakes at the appropriate level. It also has a manual override so you can apply the trailer brakes independently.
I don't think (someone correct me if I'm wrong) a typical aftermarket brake controller will work with a Tesla. The way I remember it, the aftermarket controller had a sensor or connection to the brake pedal. The harder you press the brake pedal the harder the controller would tell the trailer to brake. With a Tesla the brake pedal isn't the only way (or even the main way) you command the vehicle to decelerate. With the aftermarket brake controllers I remember, the trailer brake would not be activated when decelerating by letting off on the accelerator pedal on a Tesla vehicle.
You should be able to use an aftermarket brake controller, unless modified, it wouldn't activate except when you apply the brakes. Aftermarket controllers just get a signal that brakes are activated (brake pedal switch), then the pendulum (older controllers) or accelerometer are used to determine how hard you are braking and send the signal to the trailer brakes on how hard to apply trailer brakes.
The pendulums have been in use for decades and the accelerometers for at least a decade. They still have knob or sliding switch to activate the trailer brakes independently if needed, and have a "gain" function to dial in the strength of brake activation. They are very reliable and every travel trailer, fifth wheel and utility trailer over a couple thousand pounds, uses these systems to activate their brakes. Over the last 10-15 years, many truck and SUV manufacturers have started adding OEM integrated brake controllers as an option, they usually have a sway control feature as well (apply trailer brakes if sway detected).
Euro:
Aftermarket trailer brake controllers should work just fine on just about any vehicle.
