3:1 ratio of oil:vinegar, vinaigrette -- how can I use this in soups?

Ruhlman's ratios are very useful for baking, where the ingredients play an important role in the physical structure of the end result and a bad ratio can result in a bad cake (why didn't the bread rise?, etc.) They are OK for sauces to ensure a pleasant consistency (and partially because of the physical constraints of emulsified sauces), but much less important there. In fact, I generally make bechamel with twice as much milk as he says, and get a thinner bechamel which I find much nicer than his version. There is no structural problem with it (the way there would be if I tried to use twice the specified amount of milk in something like crepes).

In seasoning, there is no need to consult an external ratio at all. Sure, if you find exactly this ratio tasty, use it. But you can add any amount of fat and vinegar to your soup and get a good soup; your own taste preference is the only reliable guide there.

This said, it is rather unusual to add oil as a seasoning to a soup, and most Westerners don't add vinegar either. A soup is more nourishing when it has some fat, but it usually comes from the meat. It is also popular to sweat the onions (and sometimes some other long-cooking vegetables like carrots) in oil before adding the water, and the oil gets incorporated into the soup. The amount of oil in this case is judged by the onions: they should be evenly oiled, but not swim in a puddle of oil.

Some acidity usually improves a soup, and if you don't thicken with yoghurt, vinegar (or lemon juice) is a good choice. But most people who add it at all add pure vinegar when the soup is ready (to the pot or individually to each plate), and generally just add a squirt, then taste, add again, etc., until it tastes good to them. There is no ratio to follow.

I don't know of a tradition to add vinaigrette instead of vinegar of this point, but preparations containing vinaigrette are possible. For example, the garlic for tripe soup can be held either in pure vinegar or in a vinaigrette (but this is less common), and it gets spooned together with its fluid into the soup. However, if you decide that you like to use vinaigrette as a seasoning, just go ahead.

There is no point of using emulsified vinaigrette for soup (the emulsion will break). If you want to avoid fat bubbles swimming on the soup, make a thickened soup, the flour should bind them. This assumes a "standard" soup, a cream soup should have no trouble absorbing a bit of oil.

There is no need to use vinaigrette instead of pepper (although again, you can do it if that is what tastes best to you). It is better to use both, because they enrich the taste of the soup in very different ways.

The same applies to any other seasoning: no need to use a ratio, go by your own taste. Use as much pepper and salt as you like, nobody can prescribe you to like it exactly 3:1.

As for the traditional use for vinaigrette, it is a basic salad sauce. It can be used as-is, or turned into one of countless variations (actually Ruhlman explains it and gives some interesting variants). But for salads, it is preferable to emulsify it (usually with mustard), else it wilts the leaves. There was a Food lab article on that, but Ruhlman doesn't mention it and gives almost all vinaigrette recipes without mustard (except for the classic one, which of course has it).

In vinaigrette, the 3:1 oil:vinegar ratio gives it a specifically thick consistency when emulsified. That's it. This vinaigrette will lose all thickness if you add it to soup, because you're increasing the aqueous (water-containing) portion, preventing it from emulsifying.

While I suppose you could add vinaigrette to soup, as one seasoning, I think you'd be better off using straight white wine and balsamic vinegar. These add a nice touch of acid.

If you're looking for a ratio to use in soups, look at mirepoix: 1:2:1 carrot:onion:celery by weight. Then you can play with the ratio of mirepoix (by weight or volume) to water, and the amount of meat and other seasonings you add.

Note that when trying to convert your cooking to a precise recipe, a good kitchen scale (with 1g/0.1 oz precision) is critical! For spices, you can use a smaller jeweler's scale with 0.1g precision to track the weight of a spice jar; the margin of error here usually translates to under 1/8 tsp of spice, or enough to be unimportant.