Focal length is a property of the lens, not the sensor. The 35mm on your camera will appear as a 52.5mm lens (35 x 1.5) would on a full frame camera.
The thing that makes it a crop lens is the smaller image circle projected out the back to cover a smaller crop sensor. It allows the whole design to be smaller in size and weight than a lens made for full frame. But it’s the same 35mm’s as any other 35mm lens whether designed for full frame, crop, 4/3rds, or medium format.