You would do it here:
position = position + self.velocity * dt
Multiplying by dt changes the logic from “add this amount of velocity per frame” to “add this amount of velocity per second”.
You’re maybe confused by this line:
self.velocity.y = self.velocity.y - GRAVITY * dt
That one is fine because it says “reduce y velocity by this amount of gravity per second”.
Multiplying self.velocity.x by dt is meaningless.