> meaning it can fly up to 370 minutes (over 6 hours) on a single engine
It can fly almost indefinitely† on one engine. Performance is reduced, but it can even still climb. That ETOPS rating means this plane is allowed to fly routes planned at up to 370 minutes over water with two engines in the expectation that when sooner or later it experiences an engine failure the one remaining engine can get them to safety so often that regulators are willing to accept the residual risk.
If you call up the regulators and say "OK, I have an A350 here, but one of the engines doesn't work, can I fly that over an ocean to get it fixed?" they're not going to issue you a ferry exemption justified by ETOPS, they're going to say "No". ETOPS is about what you can do with two engines knowing what will happen if one fails.
† Obviously it will eventually run out of fuel. And engines can fail, although that's rare, the core idea of ETOPS is that so long as these failures are rare enough we don't need three engines.