Is there an equivalent of no-code for chemistry or biology?

Not really. There is biobricks (https://parts.igem.org/Help:An_Introduction_to_BioBricks), but you would need to have some background in biology and lab techniques to know how to use them.

I'm skeptical this would ever be a thing since doing anything non-trivial really does require understand how things work, since there are so many confounding interactions at the molecular level.

If you really want a head start you just need to start learning the fundamentals of those fields.