This is a flat, substabtial interface with the 10th Amendment’s allowance of states to manage and run elections. If a state allows elections such that they aren’t denied on account of race, gender, and people under 18, they can be run however the states deem. Requiring someone to register with the federal government is not a power of Congress
USPS likes to think of itself as completely independent. This news hasn’t even hit the organization yet, the fallout will be interesting. I can see finance and their lawyers squawking about the massive amount of lawsuits that could come out of this, as now USPS is the one harming them.