The kittens are so noisy that I can hardly hear what you are saying. Is 'that' a relative pronoun in this sentence? or Noun Clause? Can you explain in detail for both cases? thanks
The kittens are so noisy [that I can hardly hear what you are saying].
The bracketed element is a declarative content clause functioning as complement of "noisy", the head of the adjective phrase.
Although it's a complement of the head, it's actually licensed by the "so" that modifies "noisily". We know this because if the "so" is dropped the sentence becomes ungrammatical.
For this reason, it can be called an 'indirect complement'.
Note: I would advise you to drop the term 'noun clause'. The classification of finite subordinate clauses is based on their internal form rather than spurious analogies with the parts of speech.