Contracts don't, but foreign law is going to make this a pain for OpenAI. Other countries may not care what a U.S. court orders; they want their privacy laws followed.
This is why American cloud providers have legal entities outside of the US. Those have to comply with the law in the countries where they are based if they want to do business there. That's how AWS, Azure, GCP, etc. can do business in the EU. Most of that business is neatly partitioned from any exposure to US courts. There are some treaties that govern what these companies can and cannot send back to the US that some might take issue with and that are policed and scrutinized quite a bit on the EU side.
OpenAI does this as well of course. Any EU customers are going to insist on paying via an EU based entity in euros and will be talking to EU hosted LLMs with all data and logs being treated under EU law, not US law. This is not really optional for commercial use of SAAS services in the EU. To get lucrative enterprise contracts outside the US, OpenAI has no other choice but to adapt to this. If they don't, somebody else will and win those contracts.
I actually was at a defense conference in Bonn last week talking to a representative of Google Cloud. I was surprised that they were there at all because the Germans are understandably a bit paranoid about trusting US companies with hosting confidential stuff (considering some scandals a few years ago about the CIA spying on the German government a few years ago). But they actually do offer some services to the BWI, which is the part of the German army that takes care of their IT needs. And German spending on defense is of course very high right now so there are a lot of companies trying to sell in Germany, on Germany's terms. Including Google.