This debate about whether forms which are normally made into the superlative by using '-iest' can be correctly used as 'most ___' is common, including here in UsingEnglish.
Personally, I think 'more/most ___' can be used for all adjectives. It is what the morphemes '-ier/-iest' mean, and it is - I'm assuming - what came first. So I would say 'the most unhappy' is correct.
Of course not all adjectives take the morpheme ending, and there is the famous 'rule' which suggests a way of saying which do and which dont:
If it is one/two syllable(s) then the morpheme is used.
If it is more syllables then 'more/most ___' is used.
To me, this is just an observation of a pattern of language, and is by no means a 'rule' at all. Indeed, two of the most common adjectives - bad and good - don't follow it.
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