Rust

Good work.

"Just don't write bugs" ( or "Just don't write semver violations" in this case) is now rightfully recognized as a joke proposition by many (although derivative ability/experience arguments are sometimes still used, UNIRONICALLY). But it's the "better education" (or its sister magic pill "better docs") that still has many believers. So it is still valuable to explicitly make the argument for reliable automated tooling as the only real logical solution. But I digress.

if our Example enum above was #[doc(hidden)], adding a new variant would not have violated semver.

Violations in #[doc(hidden)] items should definitely trigger errors by default IMHO. To give what was a kludge in the first place more powers is not something I would call wise. Not to mention, module source code is just one click away from html docs, and it's also one click/key-combination away from a crate user's editor/IDE with LSP (rust-analyzer).

So

how #[doc(hidden)] items sometimes have semver obligations after all,

I would argue it's always the case, unless the user of the tool explicitly decides it's not.