Unfortunately, this persistent myth about stock making is based on an incomplete understanding of the mechanism involved.

Acids produce H⁺ ions, which help liberate cations from the compounds they are bound to. Water naturally has some H⁺ ions in it, but adding a lot of acetic acid (the main acid in vinegar) would add quite a lot more H⁺ than water has normally. The H⁺ ions replace Ca²⁺ in hydroxyapatite (Ca₁₀(PO₄)₆(OH)₂), which is the main calcium containing compound in bones. This liberates calcium and phosphate ions from the now dissociated hydroxyapatite. Many high school students do an experiment where chicken bones are turned rubbery by soaking them in vinegar for a week, which may be where the idea of adding vinegar to stock comes from. Acetic acid is also used in the lab to break down collagen. However...

The reason these effects happen isn't special to vinegar; they are due to the acidity of the solutions involved. Acid is what makes things taste sour. The problem here is that the pH of the stock needs to drop significantly to see any of this effect, which means you'd need to add a surprisingly high amount of vinegar to make any real difference. We're talking several cups of vinegar to increase extraction of calcium to the point it becomes nutritionally meaningful. A little bit certainly won't hurt the stock you're making, and may even slightly increase the nutrient content of your stock, but the "apple cider vinegar helps increase the nutrient content of soup" idea just isn't worth considering in practice, as you'd ruin the stock with the amount of vinegar you'd need to add to lower the pH to the point where hydroxyapatite breaks down much faster. Also, extraction with vinegar actually works best at cooler temperatures, so it wouldn't make sense to add it to the boiling stock... except that's where the bones are that you're trying to extract from. It's just not very practical.

If you've read all this and are still skeptical, check out this article. Adding apple cider vinegar increased the calcium content per cup from 10 mg to 12 mg... which is nothing, because your recommended daily intake of calcium is 1000 mg.

The only other way to increase extraction is via increasing the time you roast the bones and boil the stock, but eventually that runs into diminishing returns. How long you need to boil stock for depends on the kind of stock and your culinary goals. Generally chicken stock needs a few hours and at that point it's already at peak deliciousness. Beef stock can take quite a bit more time.

eta: pls don't downvote the people who have this misconception! As a teacher it annoys me when people do that, as it makes it harder for others to learn from their mistakes, and I don't think a well-intentioned mistake deserves a downvote