Seeking help trying to diagnose an issue with my 300CD.

I've had no mechanical issues, until the other day I had some increasingly violent shaking every time I idled. 2 red lights later the engine shut off. Was able to turn it on for just long enough to get to the gas station across the street.

I was low on fuel but not at minimum according to the gauge, maybe 10% above. That said, I replaced the cluster a few months ago and it might not be entirely accurate.

I filled up the tank but still could not get the car to start. "Choking" sound and shaking when firing the ignition.

Towed it to the mechanic where it sat for 3 days, lo and behold it starts perfectly, runs perfectly, drives perfectly.

I'm nervous to drive it without knowing what the issue was. Mechanic can't find anything wrong.

Is it possible that the tank was so empty that it needed time for the fuel to re-enter the system? I'm not sure if that makes any sense... but it's the only clue I have at this point. Any ideas are welcome and appreciated -- thanks.