Yes, bone broth fits keto comfortably. A mug of it is almost entirely water, gelatine and minerals, with barely any carbohydrate, so it will not touch your ketosis. What makes it worth bothering with is not the carb count though, it is the salt and the warmth, both of which happen to solve two of the most common early-keto complaints at once. I keep a batch in the fridge through the colder months and reach for it on the days my legs feel heavy.
Short version: a can of diet cola has essentially no carbohydrate and no sugar, so it will not knock you out of ketosis, and plenty of people drink it happily on keto. Whether it is a good idea for you personally is a slightly longer conversation, because the worries about diet soda are less about carbs and more about sweeteners, cravings and habit. Here is what actually holds up and what does not, so you can make your own call rather than follow either the “totally fine” or the “poison” camp.