This distinction isn't nearly a bright line as you think it is, the US is essentially what happens when an EU-like structure has 200+ years to evolve. In the US, States have their own constitutions, legislatures, various legal systems, and almost complete autonomy with narrow exceptions. Around 30% of them operated autonomously as their own countries at various times. Americans have almost no contact with the Federal government, only State governments, and the nature of State governments, laws, and legal systems varies quite widely across the US because they evolved independently.

As a simple illustration, the US has no national ID because the individual States have sole authority for managing the identity of their citizens. Similarly, it is why all contracts denote the State whose legal system has jurisdiction over interpretation of the contract -- there isn't a meaningful Federal jurisdiction over such things. This is also why the US Federal government can't just "pass a law" to do things, what they can actually do is severely limited by what the States feel like allowing them to do. While the States don't flex their autonomy very often these days, almost all power in the US rests with the individual States.

I don't think the line is that bright. AFAIK there are quite a few areas in which the EU is more centralized than the USA. The relationship between US states and the federal government does explain certain differences to the EU, sure. But not if you simplify it to "US states are like souvereign countries" because so are EU members. EU and USA cannot be different because of something they have in common.

> This is also why the US Federal government can't just "pass a law" to do things

In a way, it can do that by changing the constitution. That requires the consent of a majority of states, but this is common in federations. The EU cannot change its "constitution" at all except with the consensus of all members.