"Two minutes spent idling is equivalent to one mile of driving. Idling your car for 10 seconds wastes more fuel than restarting it. Today's vehicles need no more than 30 seconds to warm up in cold weather. Excessive idling can damage cylinders, spark plugs, and exhaust systems."
taken from - https://www.aacog.com/611/Be-Air-Awa...aust%20systems.
Today's modern cars don't need more than 30 seconds of warm up time. Driving slowly for a few minutes is better for your engine than letting it sit idling. I never heard of idling before you park before.
https://www.familyhandyman.com/artic...in-the-winter/
I make an effort to turn off my car for longer stops these days. If I waiting for a train to pass for example, I will turn off my car. I don't need an "auto stop & go" feature to do something like that.