One aspect that does work is framing the need for tests as assurance that specific invariants are verified and preserved

Agreed - this is the specific aspect which I hoped would be communicated by studying TDD a bit!

The team is afraid that making changes will be more difficult when tests exist, but TDD (or maybe a more specific concept like you mentioned) demonstrates that tests make future changes easier.

And I specifically advocated not to follow “write tests first”.

Name-dropping concepts actually contributes to loose credibility of any code quality effort, and works against you.

OK. If I were having an in-depth discussion with my team of fellow developers to convince them to start writing tests, I don’t think that’s name-dropping.