Stir-fry pan choices
A billion Asian households use a thin carbon steel "wok like" device to cook on quickly and efficiently. I have never seen anything work as well, or last as long. Daily use for 20+ years is normal

After the first 10 or 20 uses, the patina is well developed, and they work as intended

Buy one from a Asian food supplier for a few tens of dollars, there is no point in getting a fancy brand name one, it will not be as good

The heat transfer issue, is a factor of your burner. The heat output rating of your burner will dictate how much food you can stir fry at once. If you want to do more at once, you need a bigger burner, not a fancy pan