Adding flavorings & fillings to bread dough
As you have already intuited in your question, what you do to adjust is going to vary based on the ingredient, and how much of that ingredient you add to the bread.

I can try to address some of the specific cases you mention:

Walnuts
This generally should not be a problem with adjusting hydration, other ingredients, or cooking times, although if you add too many walnuts (or other fillers) it can make the bread fall apart more easily. If I am adding nuts to a dough, I typically stick to a quarter cup or so for a normal-sized 1 lb loaf.

Olive oil
Adding any oils or fats to your dough will fundamentally change the character of the bread. As you add more fat, the resulting bread will tend to be softer and of course oilier. The crust will also usually tend to be darker when you bake it. A standard white bread loaf might have 1-2 tbsp of butter in it, for example, whereas a brioche might have 4-5 tbsp. If you just want an olive oil flavor in your sourdough, you might consider brushing the surface of your dough before baking (this will also usually cause the bread to darken more while baking) or right after you pull it out of the oven.

Onions
This depends on the hydration of the onions, but when I use fresh, finely chopped onions I do usually lower the amount of water or other liquids in the recipe. I tend to go by the texture of the dough rather than any hard and fast rules here, but is say for a quarter cup of fresh onions I may lower the amount of water for a single loaf by a tablespoon or two. One thing I will advise is that it takes a while for the water in the onions to be incorporated into the dough; I typically add less water to start, mix the dough thoroughly for 5-6 minutes with the onions, then check the texture of the dough to see if I need to make any hydration adjustments.

Extracts
Small amounts (e.g. a quarter teaspoon) do not have a significant impact on the proofing in my experience. In fact, small amounts of alcohol are already created during fermentation, and for a typical bread yeast (or wild fermentation as is the case with a sourdough) the alcohol levels would need to reach over 10% and potentially much higher before fermentation is inhibited in any way. Link Saccharomyces cervisae or "brewing yeast" is the same type of yeast typically used in bread-making, although in sourdough you will usually also find other things that contribute to the character such as lactobacillus and pediococcus.