USPS is operated by a 11-person Board of Governors — the Postmaster General, his deputy, and nine governors appointed by the President and approved by the Senate for seven-year terms. Some of these slots are frequently empty. The Board appoints the Postmaster General, who acts as the CEO.
A separate Postal Regulatory Commission with five members appointed by the President and confirmed by the Senate oversees the USPS, including the rates it charges.
From experience, not with the USPS but still, the customer tells the carrier to prioritize. Customer as in the company buying services from the carrier, here Amazon, and notbthe customer of Amazon.
And it is up to, in this example, Amazon and USPS to make sure staffing and capacities are adequat. If you are among the top three customers of a company, you hold a lot of sway regarding prioritization. And during holiday season, stuff like that happens all the time.