It doesn't happen in Gullstrand-Painleve coordinates which would be a "correct" set of coordinates for a freely falling observer as they enter into a black hole

It doesn't happen in Gullstrand-Painleve coordinates which would be a "correct" set of coordinates for a freely falling observer as they enter into a black hole. Or the Lemaitre coordinates work too. Passing the event horizon in Schwarzschild coordinates is meaningless, it never happens.