Why would I add garlic to a recipe after onion with such a small time difference?
This is standard in most recipes. Onions take a lot longer to cook and become aromatic. Garlic does it within 30 seconds to a minute.  Three minutes is a long time for garlic. I promise you, you don't want burned garlic in your soup.
When you add the remainder of the ingredients, particularly the liquids, you reduce the direct heat that the garlic is subjected to and prevent it from burning.
Here's some supporting info from The Kitchn:

Early in our cooking career and for a long time after, we assumed that you needed to cook garlic as long as its cousin, the onion. Our results were spotty: sometimes it was ok, sometimes we picked burned bits out of our dinner. It wasn't until we got serious about cooking that we learned another way...
Whether they're being used in a quick stir fry or as the base for a soup or sauce, both onions and garlic need to be cooked at least little to get rid of their raw bite. However, while onions benefit from a longer cooking time, garlic will quickly burn and become acrid if cooked the same way.
Garlic usually does best if it's cooked quickly and over medium heat. About thirty seconds will do the trick. This is just enough time to cook off the rawness, allow the flavor to mellow into the dish, and let the aroma to hit its peak. You'll know it's done when you can smell the garlic and your mouth starts watering!
To account for these different cooking times, start the onions first, cook all the other main ingredients, and then add the garlic last. We like to clear a little spot (or &quot;clean slate&quot;) in the middle of the pan to let the garlic cook by itself for a few seconds before stirring it into the rest of the dish.