“Prompt engineering” is not really a role that exists in industry. The people who write “prompts” for things like the system prompt of chatbots or a LLM connected to an app to do a specific task are usually ML engineers who have a basic understanding of ML concepts, but also a lot of general software development experience. The task of “prompt engineering” is usually a small part of the job.
If a company is really looking for a “prompt engineer” they are most likely also looking for someone who can also implement and fine-tune models.
Many companies might require a masters or phd with papers published in journals like NeurIPS or CVPR.