This is where lawyers, regulators, and engineers can reasonably disagree with very serious consequences for governments, shareholders, and ultimately citizens.
If you're in a given geography/regulatory regime, and you read something on your smart phone, technically you were served that via some cell tower or ISP, those bits transited that infrastructure. In the US there's a massive clot of regulatory blockage working it's way slowly through the bowels of government around the term of art: "common carrier".
As with many things that devolve into nitpicking, there is a deeper issue: the EU is increasingly regretting becoming the host to, ironically, European-style colonialism on large-scale consumer Internet platforms. The PRC has its own Google, Twitter, Facebook, etc. The EU has Google, Twitter, Facebook, etc. and doesn't love that US companies and regulators are kind of driving the digital lives of the citizens.
The proximate tussle is about the durability of the storage involved. As a European regulator I might be much more comfortable with a write-through cache like TAO holding messages, or FBIDs of messages, including a German in the chat than I am with all such chats being held on a DFS in Prineville among other places, and having them ground over by a Spark or Hadoop job in Forest City among other places.
They'll kick it around and come up with some compromise that will serve end-users by accident at best. Europe won't develop a homegrown consumer Internet industry in our lifetimes. The odds are both US and EU legislators and regulators will miss a step and it'll be ByteDance everywhere by the time anyone reads this :)