Do Idioms such as “all the more” function as adjectives or adverbs?

All the more reason to value these beautiful little creatures and their habitat, right? (From TOEFL)

In the sentence above, I think "all the more" is functioning as an adjective. In Merriam-Webster dictionary, this expression is categorized as an idiom without indicating whether it is an adjective or adverb. For the example given by Webster, "The fact that they’d written the play themselves made it all the more impressive", I feel like "all the more" is used as an adverb modifying adjective impressive.

So, in effect, what grammatical part does the idiom "all the more" play?