Isn't this why companies incorporate in various nations so that they can comply with local regulations ? I'm assuming that EU will demand OpenAI to treat EU users differently..

If they did incorporate in the EU and run their servers in the EU, the EU entity will be a separate entity and (not a lawyer), I think as a result, not the entity concerned by this lawsuit.

Assuming the EU entity were a subsidiary "but I keep that data overseas" seems unlikely to get you off the hook. However I don't think you can be ordered to violate local law. That would be a weird (and I imagine expensive) situation to sort out.