If Twitter is doing business and earning money in the European Union, then it has to abide by national law - just like any other business operating in the EU.

In a scenario where Twitter doesn’t comply with the law, the European Union can fine Twitter, appropriate earnings from the European market, sue in the United States or income bilateral agreements, file for extradition, or shut down Twitter in the EU via IP ban and having the app removed from the various national app stores. Google and Apple will comply for their app stores, and European providers will comply regarding an IP ban. Some people might still be able to figure out how to access Twitter via sideloading and VPN, bit it would effectively destroy Twitter’s business in the European Union.

So yes, there’s a lot the EU can do.