Not a diaphragm, that absolutely is a menstrual disc. Do not expect them to provide contraception, but they're disposable, low footprint, and apparently comfortable. They unsettle me, I haven't tried them. The menstrual cup is in the bottom right, reusable, but the size makes them uncomfy for some folk.

Edit; Also sorry you had to deal with that. These things really should be less taboo so it's not such a baffling 'what the fuck is this shit?!' surprise when a product ends up somewhere it shouldn't.

Dogs and trashcans I am so familiar with, 'cause a dog I lived with managed to get a tampon string wrapped around her teeth and was choking on it in her throat after she got in the trash.