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I'd let supabase handle auth ++ db and use a "supabase edge scheduled function" to execute your script.

it seems to me that supabase would cover only the backend (auth, storage, db etc.) and not the frontend part though

True, but anybody can host the frontend... which is some HTML with a few calls to supabase.

I am more concerned about having an easy way to develop the frontend, more than where to host it.