What is the ruling on working in a supermarket that sells both prohibited and permissible items, while committing to working only in the permissible sections and not dealing with the prohibited items in any way, due to the unavailability of other work?

We are pleased with your question, which indicates your pursuit of what is lawful and avoidance of what is doubtful. Your work in the supermarket is permissible, provided you avoid the forbidden things you mentioned and your work does not involve assisting in anything unlawful.