If the point is to reduce carbs/glycemic load, then gums are an option. These are primarily fiber, so they don't "count" as carbs nutritionally, although they are technically carbs (chains of carbon-based molecules- it's just that these are chains our bodies can't digest or use the energy from.) There's xanthan gum, guar gum, and probably a few others I can't think of the names of right now. Personally I've only used xanthan gum.
You can use xanthan gum pretty much anywhere you'd use flour for thickening a gravy or soup. You need to dissolve it REALLY WELL in cold liquid before adding it to a hot liquid, and then stir thoroughly while it's thickening. If you don't do it right, you get clumpy "gummy" spots floating in a thinner liquid, rather than a smooth thick liquid all around. It works best (smoothest results) when combined with a starchy thickener, so you can use less of the starch.
Eggs (or at least egg yolks) can also be used to thicken sauces. This basically involves cooking the eggs in the liquid so it all thickens up together. I've never done it (except for egg drop soup), so I'm not sure of the exact technique. I'm not sure if it works with whole eggs or just yolks, but I'm pretty sure it involves mixing with a cold liquid first and then adding to the larger mix of hot liquid and stirring while it thickens. I'd suggest searching for "low carb recipes" online and you'll probably find a bunch of recipes that explain these techniques better than I can.
Egg drop soup is made by having broth (I use chicken and/or turkey, whichever I have on hand) heating up, then stir in some beaten eggs and gently stir while the eggs cook. For this recipe you DON'T want a smooth texture, you want pieces of cooked egg floating in a thin broth, but the end result is definitely a thicker soup than plain old chicken broth. IME, egg drop soup is a nice comfort food, and a perfect replacement for chicken soup with rice or noodles. I generally use 2 eggs per pint of soup.
Oh, back to your question about bone broths- they are an EXCELLENT source of minerals, protein, and fats, and are extremely low in carbs (even when cooked with veggies.) They're very satisfying and leave you (well, they leave me anyway) less likely to seek out starches to feel full.