That has not been true since the Lisbon treaty. Now, it’s an EU-wide government supreme over the EU national governments. In key respects, the EU is even more powerful compared to the EU national governments than the US federal government is compared to the US state governments. For example, the federal government cannot pass laws then force the state governments to enforce them. The EU can.
If the EU stayed on its pre-Brexit track, all the stuff that renders US politics intractable would be coming to the EU faster than anyone would think. You’re already seeing it—for example, with Sweden and Finland having to strengthen gun control to accommodate the sensibilities of the rest of Europe.