> Much like any other automatic car??
By "automatic" are you referring specifically to a slush-box? The car in question has an S-tronic (aka DSG) gearbox, which is more akin to two manual boxes welded together.
Frankly, I don't understand why it was trying to lurch forward. Perhaps on the A3 brake hold is an option? Normally, once you've come to a stop it should keep enough brake force applied to keep the car from moving (forwards to backwards) even if you lift your foot off the pedal.
The other thing is that most cars tend to come with auto start/stop these days so unless it was not at normal operating temperature, running the AC/heater, charging the battery, or whatever, the engine would usually stop anyway.
Alternatively, there might be an option in the settings called "coasting", which will disengage the clutches when, well, coasting or stopped.
But in any case, it's good practise to shift to N while at traffic lights if the engine is still running. It's easier on the transmission and prevents it from overheating in extreme cases.
> So much so that most automatics these days don't even let you start the engine without your foot on the brake.
That's nothing to do with the transmission type. Manual cars are the same, and it's intended as a safety feature.