AI, RGPD/DSA/etc, yearly money laundering regs are a good example. They come on top of local regulations, they don't replace them. Each country still has its own special laws.

The original EEC was to help maintain peace through economic interdependency. Now the EU is very different with ultimate goal of full integration, i.e. a federal state. The single market is a step, the single currency is another step, EU Parliament, tax rules, now possibly defence matters, etc. Step by step but always in the same direction.

The EU started with the coal and steel initiative, which created a common market for those commodities. It was indeed "peace through trade", but mainly trade.

And the goalpost has since moved very far, I don't see really how preventing countries from sending back illegal immigrants or making same-sex marriage has anything to do with European peace.

The problem is that it also prevents countries from reducing the regulations in order to foster local innovation, avoid disadvantageous rules (there are more lobbyists than bureaucrats in Brussels, for a reason) or adapt to a new reality (AI being a good case). Moreover, each country still have their own specific laws, the EU regs come on top, and don't decrease the amount of laws. And the EU votes a lot of laws, since its the main power it has, on average 7 per day.