The Rutger Hauer film Omega Doom had a lot of black trenchcoats. The “robots” in particular wore sunglasses. A lot of visuals like this that are similar to The Matrix. It came out in 1996, three years before.
Lots of drawn out pan or zoom shots. Don’t recall for sure any slo-mo.
Well, if we’re being pedantic … I honestly don’t think you can make that clear a distinction. Both trench coats and dusters have varied quite a bit, over the years, with considerable crossover between them. Neo’s coat isn’t a classic example of either, to my mind — it’s just a long coat. He does wear a cassock right at the end of the film, and in the sequel, but the iconic look is definitely a coat.
Re the OP: I don’t think you’ll find a single origin. What there is, is a chain of influences, crossing cultures and media, taking in comic books, anime and manga, film, television and pop videos. Look at the original Highlander, directed by Russell Mulcahy, and his earlier video for Ultravox’s Vienna. He later directed The Shadow, based on a 30s pulp fiction hero — who dressed in a long black coat.
I think the faceless bad guys is where to look. I was trying to think of actors in lead roles. My first thought was Le Samourai or a noir film. The problem is leading men, especially good looking ones, don’t seem to like wearing sunglasses, they want their eyes on-screen. Also the black trench coat seems to be a recent development. It always seems to be a buff trench coat or a black suit.