"It triggers the warning when the spoilers are unlocked and the
airspeed
exceeds 25 knots."

The same conditions are satisfied for landing approach with the gear
down. I expect the answer is that the 302, containing a full airdata
and GPS system, can easily determine that a takeoff has started.
Indeed, it does that to start the logger function.

I use the airbrake warning of the 302 as well. It usually bitches at
me for just one cycle on takeoff as I always use the airbrakes until I
have good aileron control.

Andy