> I'm wondering if it's a colloquialism like saying 'the kettle has boiled' where we clearly mean that the water in the kettle has boiled rather than that the metal of the kettle has become molten.
Exactly this. I've also heard of used as (enough) the positive kind. You could also translate it as:
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> There's enough/a lot (hot)water in the bath
If you scroll the definitions a bit, you'll find things like, full, a lot, much, entire. Better to remember these kind of sentances as is.
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> Is there any difference between this and the original in nuance?
I think your example is correct but, the original is more natural where as in the second example you are just pointing out that the bath is filled with hot water for some different reason, I guess?