Yes, I fully understand the functioning, I was just trying to keep things simple. Even Europeans don't understand this, Americans must be lost. "Council of the EU" vs "EU Council" is next-level opacity. Since the latter doesn't technically exist, I find it helpful as a less syllabic synonym for the former (where it can sit neatly alongside EU Parliament and EU Commission, leaving nobody confused). That leaves the European Council, i.e. the periodic flagship permutation of the Council. This is indeed a senate-like entity in Montesquieuian terms, that wasn't my idea.

Obviously I agree with all your other points.