The problem with schizo tech is that there are so many technologies that are contingent on other technologies.
You can't do advanced biotech* without electronic computers to sequence DNA quickly, for instance.
*or at least reliably and consistently
Not quickly, or reliably, true, but genome mapping is entirely possible with the application of basic mendelian laws. Scientists were able to map the chromosomes of fruit flies just by using statistical analysis and breeding. Now, breeding flies is different than breeding crops or or cattle, but similar techniques could (and have) been used to produce genetic maps comparable to those of computers. The discovery of the more fine genetic machinery, including DNA itself, would take until the 20th century, but heredity is easy enough.
Once you have microscopes to observe cell cycles, mathematical tools to do the calculations, laboratory protocols, and good model organisms (there was a reason why Mendel choose pea plants and Morgan fruit flies: they have conspicous genetic traits and are easy to breed), you're halfway to discovering heredity and genetics. It could have been potentially discovered soon after the microscope.
True genetic engineering, however, would probably need computation, that's true. The understanding of DNA structure requires more advanced techniques. But once you have good enough microscopes, you can start to deduce the basics.
As for evolution, there were many people in antiquity and the middle ages who had similar thoughts. However, IMHO, you need to have a society that has determined an old age for the Earth, and has become interested in paleontology and natural sciences. From there, the dots connect themselves. I actually think that non-European societies might have even an easier time on accepting an old Earth and the kinship of humans with other forms of life.
Ecology has always existed as a natural science, as long as people have observed nature ('Natural History'). A rational, predictive and scientific understanding of nature depends on mathematical and statistical tools to predict population behavior and resource usage. Not outside the realm of any society with advanced enough mathematics.