Here are a few reasons why I think biotechnology would lag behind.
1 Computer Technology Advanced so Fast Other Fields Stagnated
Technology in other areas such as computer technology has picked up speed so fast that there is little if any time or research devoted to other fields.
When technology grows, it does so at an exponential rate. Faster computers are able to use their better processing power to make even stronger computers than before. Perhaps, in this world, computer technology grew at such an exponential rate that it overtook all other industries. In fact, what if technology grew so fast that people are no longer needed for the process anymore.
AI is so advanced that there is no need for humans in the process anymore. The AI makes more computers and more advanced AI, so those can then make even more advanced AI.
Why would artificial intelligence care about learning more about biology when it can focus on making more powerful and intelligent versions of itself? The AI in charge of research is sentient enough that it does not care about biology. t refuses to teach the people anything about it and refuses to let anyone learn about it.
Because of this, technology has developed to only be focused on artificial design and nothing biological.
2 Greed of Certain Corporations
If you don't have a slightly malicious AI roaming about to keep people from making biotech, simply have some sort of rich corporation keeping people from doing it.
The layout of this world has all the technology development run by one or more major corporations that have a tight stranglehold on what can or cannot be produced. They specialize in making computers and other similar devices, and they view any firm that does not fall in line with their designs gets scrapped because it is viewed as competition.
Why let medical research advance when you can continue to let people pay exorbitant prices for procedures that would be super simple in our world? Sure, the computers are powerful enough that the rich people could theoretically heal themselves or get fancy prosthetics, but the poor people are never going to get their hands on that stuff. Money is a key motivator. If the rich believe they can make more money by halting the advancement of biotechnology, then they will and no one will be able to stop them.
Also, the corporations only want people to be part of their development teams. They don't want people researching something that won't profit them, so they just train people from a young age to only care about computer science. Any textbooks on biotechnology are censored or simply destroyed and anyone that tries to talk about it or research it gets silenced or at the very least paid off to not speak about their findings. That way the computer manufacturers eliminate what they see as competition and keep the best goods for themselves.
3 There was a Horrible War Using Biotechnology
In the past, biotechnology was incredibly advanced. It was used to make horrible toxins that wiped out entire cities in seconds and monsters that only deserve to exist in nightmares. The war that inspired the creation of these terrors nearly wiped out everyone, so the frightened people did their best to rebuild after everything was over, and, years later, we get to how the world is now.
Knowledge of biotechnology no longer exists for two reasons. On one hand, a lot of the progress was lost from the war. Leading biologists were killed by their own creations and most of their research was destroyed.
Also, the current regime refuses to let anyone learn the secrets of the war. Biotechnology is a taboo subject because it brings up the terrors of the time in the past. The regime destroys any mention of the technology that caused the war, along with any biology textbooks. Biology is no longer taught in schools, or at least only at a basic level. Kids aren't even taught what a cell is anymore. As the generations go by, it goes from willful ignorance to people being genuinely illiterate in the field of biology. Even the elites hiding this knowledge don't really get it anymore. Ask a person what DNA is and they give you a weird look. They have no clue, because that's how repressed knowledge has become.