Look up an old movie called 'Altered States' Neuroscientist has been experimenting with sensory deprivation and then tries peyote before going into the tank.
This isn’t technically fully biopunk because space ships and stuff, but the biology of the world in Prospector plays a huge role and I’d definitely recommend seeing it in part just because of how well they did portraying an alien world with a lot of weird alien quirks to it.
I would reckon it’s analogous to steam, arcane, or solar punk. Where the technology and society of the world is primarily if not ubiquitously based around the concept in question, so biopunk would be a world where biological enhancement and biotech are central
The only movie I can think of off the top of my head is eXistenZ
Society. Except it's not punk, it's the rich who are a different species.
Species. The first film is just Humans making a massive mistake about alien contagion, but the sequels, lower and lower budget, "democratize" the alien infection. So many tentacle babies. Everyone can have one.
The best that comes to mind is Crimes of the Future. There are people growing new organs and altering their digestive system to eat plastic.
The book Borne was supposed to get a movie or TV show adaptation at some point. I really hope they make this well cause that's one of the best examples in my opinion.