How do I make egg drop soup thick and golden?

I think you need a better broth.

For a satisfying soup, you will want a broth that is not only thick but flavorful. Additionally, the salt can give an impression of thickness - lack of salt can make a soup taste watery even if the thickness does not actually change when salt is added. The gold color probably comes from a chicken broth, in the original recipe, although you might use vegetable broth or something if you prefer. And you might not get exactly the same color if it was due to a specific recipe of broth - or the addition of food coloring - but you can still get a nice golden color if you pick a good broth, and perhaps enhance the color a bit with turmeric or even saffron if you really want. If you start with a hearty broth, with a bright color and plenty of flavor, you will be half way to your soup.

A good broth will already be a little thicker from flavorful compounds simmered out of your stock ingredients - not much, but the more thickness comes from the flavor in the soup, the less you will need to add in cornstarch. A homemade stock will be the best, thick and rich to your specifications with lots of fibers and juices from your ingredients to thicken the stock. A store-bought stock will be convenient, consistent, and pretty flavorful - although it will have some of the thickness filtered out and replaced with thickeners, it will also the benefit of some flavoring agents. Using bullion cubes or powders as a base is still pretty workable - I have made good egg drop soup with them, but will be thinner since the process reduces the flavors to their most compact and concentrated from, and you may be missing out some of the natural fillers and thickeners that form in broth as it is made.

Each option has its plusses and minuses, you can pick which option serves you taste and convenience. Whichever you choose, you may want your broth to be a little more concentrated for this soup, perhaps reducing a store-bought broth through simmering or adding extra base (bullion cube or what you have on hand) for the same amount of water - the flavor will be a little bit diluted with the addition of cornstarch and cold water in the slurry.

Then, you can thicken your broth still more with cornstarch (at the correct stage in the recipe, of course). Make a slurry with the cornstarch and cold water, mix it to make sure it's dissolved, and slowly pour into your soup, mixing well. You should bring the soup to a simmer afterwards, for at least a minute, while the cornstarch works and thickens - but not too much longer, or it can thin again as the cornstarch overcooks.

Your milky thinner broth might not have cooked long enough to activate the cornstarch, since it is very pale in the slurry, or you might have overcooked it so even a lot was much less effective - I usually don't notice a big color change from the amount of cornstarch to a broth unless I'm using a lot, it seems to me to clear up a bit as it cooks.