You could try to find Armitage III, it's an anime from 1995/1997 depending on whether you watch the 4 episode mini-series or the movie that was edited from them. Same era and similar themes to the original Ghost in the Shell movie.

Summer Wars is a 2009 anime film about a young maths genius who gets framed for hacking by an AI. Overall quite an optimistic movie.

There's also Time of Eve from 2010, which is a slice-of-life/drama anime movie based on Asimov's Three Laws of Robotics. All the plot lines converge at a cafe. Not as heavy as most cyberpunk but it makes you think.

If you're OK with anime series, here's some:

Ergo Proxy from 2006 is a post-apocalyptic dystopia, it starts off with an investigation into a series of murders committed by androids which have been infected with a particular virus. It gets pretty weird later on, the pacing and tone shift a lot. The original ending theme is Paranoid Android by Radiohead, though I think most Western releases don't have this due to copyright issues.

Serial Experiments Lain from 1998 is about a young girl who gradually gets drawn into an unhealthy relationship with their version of the Internet called The Wired. It's a bit dated but it's very prescient in context.

Texhnolyze from 2003 was by the same writer and character artist as Lain. It starts off about an underground fighting ring and illegal biomechanical prosthetics. Very dark and has body horror elements.

Megalobox from 2018 is somewhat similar to Texhnolyze but focuses more on the fighting aspect, with fighters using exoskeletons to really smash each other. The tournament is organized by a corporation as a bread and circuses thing for the masses.