Are there common culinary uses for the addition of stearic acid?

Its main "culinary" use is as a binder or texture agent in "processed" foods. You'll tend to find it in stuff like chewing gum, edible wax, and various candy elements like coatings.

Aside from its natural occurrence (which, as noted in comments, comes in sorts of foods, but especially animal and vegetable oils and fats), it is also sometimes found in substances that are trying to mimic those oils or fats, like artificial butter flavoring, etc.

As a long-chain fatty acid, its solubility in water is limited, so it can't really be used as an "acid" in the way you tend to think about culinary stuff like vinegar or citric acid. (And its effective pH would be way too high to do anything.) The "fatty" part of the carbon chain also dominates the perceptual aspect of it, so it will taste more "fatty" than sour or acidic.

It's easy to get confused about the terminology here. Online the terms are often misused, or at least used in an ambiguous way. Some definitions:

“Stearate” is a common structural component of triglycerides (the common form of nutritive fat). In fats, it is a saturated 18-carbon chain attached by an ester linkage to a glycerol unit, along with two other such chains. Inside fats, it's part of an ester, not an acid, and it's not the whole molecule.

Sodium stearate is a free compound, a salt obtained when triglycerides are saponified (turned into soap), or broken into pieces with alkali like sodium hydroxide. From a single triglyceride fat, you'd get three fatty acid salts and one neutral molecule of glycerin. (Glycerin has several important uses in food chemistry, as a humectant, sweetener, and lubricant.) These fatty acid salts have polar (electrically charged) and non-polar ends, making them great emulsifiers, and also soaps (which work the same way). The non-polar ends will dissolve in things like other fats and greases, and the polar end will point out on the surface where it can stick to water molecules (also polar), forming water soluble micelles. This is how soaps can wash away non-water soluble greases, through emulsification. However, as an emulsifier for food, fatty acid salts are undesirable because they are weakly alkaline, or basic, like soap. They're also bitter like soaps. For food, an emulsifier like lecithin is preferred (in lecithin, the polar end carries both positive and negative charges, so that end mixes well with water, but with a net zero charge its flavor is neutral).

Stearic acid is a free molecule made by neutralizing the sodium stearate. It is a weak acid, about as able to ionize as the acetic acid in vinegar (only about 1% when dissolved). But because the acid end is such a tiny part of the much larger stearic acid molecule (acetic acid has a 2 carbon long non-polar chain, while stearic acid's carbon chain is 18 carbons long), it's very insoluble. It's metabolized the same way as triglycerides, so it's non-toxic. It's approved for a use as a food additive, though I don't know exactly for what - probably a lubricating or softening agent. Because it's so insoluble, and large, its flavor is neutral - it would need to dissolve to ionize. Shorter chain fatty acids can have objectionable flavors and odors - “prolonged mammalian unwashedness”, as I remember my old organic textbook describing it.

Since natural fats are generally quite mixed in terms of the length of their chains (stearic, palmitic, etc.), the free stearic acid wouldn't be pure unless another step was taken, like distillation. But the mixture wouldn't behave much differently from the pure compound.

You'll often see the stearate structure inside a triglyceride fat referred to as “stearic acid”, which causes much confusion when people equate the two.