Over time the large menagerie of inter-European organizations got merged into the EU. For example Euratom is the only former EC body that hasn't been incorporated into the EU completely and even then it's mostly still controlled by EU institutions. All the former trading alliances were absorbed into the EU or are now moribund. And new such organisations aren't being set up - if countries want to work together on something, like vaccines, the EU immediately steps in and takes control.

The EU is controlled on a day to day basis by the President of the Commission. Yes, the Council theoretically selects the head of the Commission although because we have no idea how they do that, and because the outcome always seems to be some stitchup between France and Germany, it's very hard to say to what extent the Council really does control that process.

And as for the Parliament, please. It cannot actually change the law, which means it's not a Parliament at all. It just calls itself that. It can only rubber stamp whatever the Commission wants to do, which it always does because the only people who want to take part in a fake Parliament are groupies who think the EU shits rainbows. And even then, the Commission can and usually does just bypass it. None of the changes to "equivalence" I've talked about required the Parliament to do anything, to pick just one example. The Commission just announces it, and it's done. It's by far the world's most powerful executive and there are basically no working controls on its behaviour, even by Treaty, which is often ignored when convenient.