"Groups of workers with higher status get paid better." True. But what is the main direction of causation here?

According to basic economics, workers will get paid their marginal product (how much you add to production). This is a pretty good first approximation. Of course, you can get paid in many ways- money, flexible hours, even status. The higher the status of a job the less it needs to pay to attract workers; this is called a compensating differential. High-level politicians are very high-status but don't make that much. Conversely, very low-status jobs (like janitor or garbageman) have to pay a bit more in money wages to get people to work.