There aren’t direct elections by the people like in countries, things are a bit more complex

It's as complex as most elections in countries that have territory based representation. My local elections are actually more complex than the EU elections. Also for that matter, if I move across the EU to a different country, I have immediate voting rights in municipal elections.

Also not everything that the parliaments says is required to be enforced in member states.

Only regulations. The EU has the power to override national legislatures if it so wishes, and it uses that power regularly, like with the GDPR. The point is it isn't up to the member states to decide what to enforce, the EU decides where it leaves leeway and where it doesn't. In some aspects, that ties member states together tighter than US states, as the US federal govt can't regulate some matters even if it wants without amending the constitution IIRC.

The founding treaties of the EU don’t allow for the creation of a European army

You got me there, the EU does not have a standing shared army, but there is nothing prohibiting it either IIRC. There are EU Battlegroups that can be called up in days which are then under joint EU command, and many member states share military resources. Stuff is trending towards a shared army as well, with the recent merging of Dutch and German armies for example. There is a joint defence and security policy as well, and forces under joint EU command have undertaken dozens of missions across the world.