If EU would introduce such legislation, it could potentially make software doing end2end encryption illegal. In such case, google would be removing it from EU Play Stores, and this would be more/less end of such messaging apps unless they comply. :-)
This is why it's important to have a reasonable legislature and laws.
And multiple points of control. In the EU the council acts as a check on populism through parliament (even if the nazis took over parliament it wouldn't give them a lot of power), parliament acts as a check on the council (even if the heads of 70% of EU countries decided something, parliament gets its say). Neither of those are the executive so they would be unable to push through laws which favour specific countries or groups of countries (as the commission are supposed to act primarily on behalf of the union, in the same way the US president is supposed to not favour his home state). Then outside of government you have the judiciary who look at the laws passed and interpret them in line with other laws, throwing out ones which are incompatible.
If you have to ask governments for permission then that's a bad design and your system will be taken away from you when the next think-of-the-children populists are elected
If you work on the assumption all governments are eternally nice and well interventioned .. then E2E chat systems aren't all that necessary in the first place