What is valued more in the data science job market, statistical analysis or data processing?
Given your current situation, a data analyst or scientist position makes more sense, but with some practice you can acquire the software skills to become a data- or machine learning engineer. There is a glut of people from academia similar to you, and software companies want people who can actually build software, so it is not surprising you see demand for engineers. But that does not mean you have to become one. Do you want to build software products?

My recommendation would be to make sure you are familiar enough with common applications of statistics in industry (e.g., A/B testing, and time series forecasting) to get a job in analysis, then learn computer science on the side. There is a wide range of salaries, depending on seniority, company and location. You can find specific figures on sites like LinkedIn, Glassdoor, Paysa, Payscale.