I like Vesper (2022) as one of the few I know of that focuses on biological technology, and it is part of the story as opposed to a backdrop.
There's a lot of body horrror/Cronenburg stuff I like that gets close. Stuff like The Fly, Testuo the Iron Man, Videodrome, etc. But that's focused more on the "wouldn't this be fucked up?" than the exploration of biotech.
Repo Men (2010) and Repo! The Genetic Opera (2008) have a strong focus on the commoditization of the human body and organs especially. Gattaca (1997) is a little similar in that genetic therapy is important to society. And The Island (2005) is centered on cloning. Of these four, I like Repo! the most, but for other reasons than its take on Biopunk.
eXistenZ (1999) is probably Cronenburg's most straight forward take of biology as technology, as opposed to just a source of horror, but I haven't actually watched this one yet.
District 9 (2009) and Akira (1988) have situations that cause massive biological change, but not centered on Biopunk in my opinion.
The Blade Runner films, despite being the posterboys of Cyberpunk film, have a lot of potential considering that at the end of the day Replicants are biological. Splice (2009) at least focuses on the actual development of new biological technology, but winds up being more of a Frankenstein tale than anything.
The Alien universe has hints of this with the Space Jockeys, xenomorphs, and androids. But it's not ubiquitous.
Fun fact: Alien, Blade Runner, and Serenity are all in the same universe apparently. Things like the Weyland-Yutani Corporation appear in all 3 films.
This also means that Predator is in the same universe.
Weyland-Yutani is in Firefly, Blade Runner, and Alien, therefore, a reaver vs alien vs predator vs humans vs android fight is a possibility.
Johnny Mnemonic sort of blurs the cyberpunk / biopunk line a bit, since Molly is a main character.
Alita: Battle Angel is a fun exploration into Bio modification as well as the hero’s journey. The first season of Altered Carbon also comes to mind, although the biomodification concept is in the lore, and not explicitly seen on screen. If you haven’t seen it, you can stop after the 1st season because the 2nd season is pretty garbage.