Contrast this to the EU where all treaties are automatically law across all members.

That's not how the EU works. As an example take the Mercosur treaty: it has 4 parts. The first post is straight up trade rules, an area that the Eau member states delegated to the EU. This part was directly valid once signed.

The other three parts all concern areas not delegated to the EU. To become law, all three parts have to be approved by the EU parliament and the EU council (which consists of the heads of the executives of the member states) and the local parliaments of the member states. Depending on local law, even regional parliaments have to approve it (Belgium is such a state). The final implementation of Mercosur is not expected before 2028.

Everything needs to pass local parliaments in EU as well.