Do companies like this have a need for SWEs? Are there opportunities for a backend SWE without any background in hardware or biology?
Of course they do. Biology and medical research can't get enough software people. But they're not as well funded as advertising or spying companies, for example, so you might have to take a significant pay cut.
I wouldn't pigeon hole yourself as a "backend engineer". Why do people do that? Software is software. The bit that matters is the core model and algorithms etc. Whether it's exposed as a web server, a CLI or just a library is a peripheral detail.
It's totally possible for a decent software engineer to learn just enough biology to get by. The limiting factor might be your interest, though. But if you have that then go for it. Get a book on genomics right now.