Claude does at least use the British English version of the phrase to me - not sure whether its picking up a language setting or reacting to my spelling etc. The American version does sound odd over hear.
"Belt and braces" (UK) vs. "belt and suspenders" (US). I'm pretty sure the phrases have the same meaning, they just use a different word to refer to the thing that holds pants|trousers up.
And the word "suspenders" in British English means what Americans would call a garter belt, hence it sounding particularly odd over here.
That is what I had in mind. I was also wondering what American call them so thanks for answering that.
Americans call bum bags fanny packs. Always raises a smile.