See LinkedIn for available opportunities. There is a Bio-Technopark in Schlieren with companies that may interest you. For example, CDR-Life or Molecular Partners.
Molecular Partners seems to be looking for a research associate in cell biology. Could be a good fit.
Basel could be a better place for career in biotech (Roche, Novartis), but Zurich is not bad either. Keep applying and don't be discouraged. It takes time and dedication... Switzerland is pretty competitive