it’s both used to describe a diet of non-animal by/products and the broader social movement of advocating against the same
Actually, in circles where "carnist" would be used, "vegan" has a very clear distinction, and it's the latter. Whether they've seen it or not, veganism in those circles will be roughly the Vegan Society's definition*:
Veganism is a philosophy and way of living which seeks to exclude—as far as is possible and practicable—all forms of exploitation of, and cruelty to, animals for food, clothing or any other purpose; and by extension, promotes the development and use of animal-free alternatives for the benefit of animals, humans and the environment. In dietary terms [which we don't use] it denotes the practice of dispensing with all products derived wholly or partly from animals.
Somebody who's solely on a plant-based diet (i.e. abstaining from animal products in their food) would be called just that: "plant-based". The reason "carnist" is used is, like I said, to denote active support for the ideology and not just passive consumption. Plenty of people will go their entire lives without meaningfully engaging with the ideology behind the food they eat, the clothes they wear, etc., which is where the "omnivore" and "carnist" terms come in.
"Carnism" makes veganism a lot easier to discuss, because simply "vegan or non-vegan" places carnism in a position of inherent normalcy. Imagine another movement (especially a minority one) that could only describe anyone in terms of "us or non-us". Positioning carnism as an ideology (which it objectively is) challenges its otherwise unchallenged position.
* Notably, The Vegan Society is the origin of both meanings.