Romance, as pointed out, is a type of fiction, comprising idealized love, chivalry, obsessive association with somebody or some idea, and mysterious adventures.
None of this characterizes Pride & Prejudice. It's a novel about manners, gossip, social mores, money, class... there's about ONE paragraph devoted to Elizabeth's realization that Darcy does indeed seem to be a man she could love, much to her surprise. There's nothing idealized about it, there are no examples of chivalry (unless Darcy paying off Wickham to marry the little tart of a sister is on par with a white knight galloping up with sword drawn.) There's nothing mysterious. This is just nonsense, putting P&P in this category.
FWIW, my lit profs, many moons ago, considered it a romance in the literary sense of the word. I do, too. No matter how it’s catigorized, I enjoy it, too. And I have a lovely hard cover edition of it with deckle edges.