What is the right course of action now?

At a level crossing you must never enter the crossing area if you cannot clear it completely. The safe rule of thumb in Germany is: only drive onto the tracks when you are sure you can pass over them without stopping.

That is why waiting in front of the level crossing is correct. You stop before the crossing (at the stop line if there is one, otherwise in front of the barrier/at a safe distance), keep the crossing area free, and wait until the red lights stop flashing and any barriers are fully open again.

Waiting “at the tracks” would mean stopping too far forward, possibly on the dangerous area near or even on the rails. “Carefully cross the tracks” is only allowed when the warning system is not active and the way across is clearly free; a flashing red light at a level crossing has the meaning of “stop” in Germany, so you are not allowed to proceed at all.