I’m curious what they mean by “expression-level syntax” specifically, because they certainly added a lot of syntax that isn’t ECMA and aren’t just Babel, backporting future ECMA features.

As long as it's stage 3 EcmaScript, I (and the TS team, AFAIK) wouldn't count that as TS syntax - that's actual ES for all intents and purposes.

Other than that it's mostly syntax that affects how your code runs - i.e. if you were to remove all syntax that TS adds, the code should still run without further modifications in any interpreter that understands ES. (And features like enums don't satisfy this condition, hence why they don't match TS's design goals.)