I would be surprised beyond belief if some combination of Savage Worlds Adventure Edition + East Texas University setting, or SWADE + Rippers setting, or SWADE + Deadlands Noir setting couldn't meet your requirements.
If it were me, I'd pull SWADE + ETU + Deadlands Noir off my shelf and go.
If that wasn't enough, I might reach for Trail of Cthulhu and the Horror Companion next.
Edit: Interface Zero also has a ton of fun gear, edges, and psionic stuff to go with urban paranomal style of play, even if you don't want to lean into the cyberpunk tropes.
I have no idea what any of those references are.
So you said you looked at Savage Worlds but stated it was too generic. If you're looking at just the straight core rules, then yes, I imagine you'd feel it was too sparse or not really "baked" to run the type of urban fantasy you've described.
The way Savage Worlds normally works is you take the core rules and apply an appropriate setting overlay that goes with it---and there are dozens of officially supported settings, and hundreds of unofficial fan mods out there.
Savage Worlds settings extend the core rules with additional character edges and skills to focus the action on the premise at hand.
The three settings I've described are all officially supported settings that contain elements of the kind of urban fantasy you described.
East Texas University (ETU for short) is an official setting created by the publisher of Savage Worlds' (Pinnacle Entertainment Games, or PEG). It's a mashup of "
Buffy the Vampire Slayer, Supernatural, and
I Know What You Did Last Summer," set in a fictional east Texas college town.
Rippers Resurrected is PEG's official setting that emulates "Jack the Ripper" / "Van Helsing" take on Victorian gothic horror.
Deadlands Noir is PEG's official setting that takes their "Weird West" setting of
Deadlands and transposes it into semi-modern 1930s Depression-era. Think, "New Orleans voodoo cults and Cthulhu mythos packaged up with Godfather-style mobsters and private eyes."
A couple more I didn't even think of that are "unofficial" published settings ---
Agents of Oblivion is very much in line with a
Night's Black Agents style of game for Savage Worlds---spy vs. spy, spy vs. supernatural, or both, in a clandestine world.
If you want to go into a more
Agents of Shield / G.I. Joe direction, check out
Freedom Squadron on DriveThruRPG.
And one more I mentioned is
Interface Zero, which leans into cyberpunk more than urban fantasy, but it has a lot of paranormal/psionic type gameplay elements, and a ton of investigative / "criminal underground" elements that could be useful as well. If I were going to do
Blade Runner style gaming with Savage Worlds, it's what I'd turn to.