If "e2echat.com" has no method to explicitly forbid your browser from accepting eIDAS certs (via a DNS record or something) then your browser will just blindly accept the compromised cert when attacked.
Wouldn't a client certificate from e2echat protect that kind of attack ? Since even when a man in the middle offers u a server cert u accept, the e2echat servers can't validate the client certificate from you anymore
(Still bad but would at least protect connections from ever talking to e2echats servers)
This forces browsers to accept all the CAs approved by the EU states, and you can be certain that some of them will be used for decrypting (and if needed modifying) the traffic
And then you can just tell the browser to not trust those CAs and you are safe. This is nothing like "chat control". This only lets the government spy on people who don't care if the government spies on them.
(Still bad but would at least protect connections from ever talking to e2echats servers)