Joining the chorus, the #1 thing you can do to improve your soup is to use a base of stock, not water. If you buy a box of stock, it will still be better than water, but if you want excellent soup, make your own stock. You can make a large quantity, as I do, and freeze it for when it’s needed, and the secret to making great stock is time. Don’t rush it.
Look, I have a friend who buys a rotisserie chicken, has it for dinner over a night or two, puts the bones in a pot, throws in vegetables, strains it after an hour, adds some reserved chicken, and calls it a day. My chicken stock starts where her soup begins. After roasting a chicken, the bones go into a pot with vegetables, and simmer for 4–6 hours, until the bones are falling to pieces. While it seems like a long time to cook something, you can binge watch a thing, or read a book, or have friends in for a glass of wine while this is going on; it requires no intervention, except to occasionally adjust the heat. Then strain, let it cool, and put it in containers for later use. You have stock.
The same principle applies for vegetable stock, or “bone broth.”
When you finally make your soup, sauté your vegetables first, add your spices and aromatics, and then add your stock. This will make a much better soup with deeper flavors than throwing raw ingredients into the stock.
To recap: use stock, sauté your ingredients before adding liquid to the pot.