yet = II. Senses relating to time.
2.a. (a) Implying continuance from a previous time up to and at the present (or some stated) time: Now as until now (or then as until then): = still adv. 4a. Often also implying contrast to a future or subsequent state more emphatically expressed by as yet (7a) [...]
Please help me dig deeper than definition 7 above, which I already understand and ask NOT about.
Question 1: OED pinpointed the right definitions of yet (an adverb, adjective, or conjunction) in as yet, but it doesn't identify the lexical category. So which lexical category is yet?
Question 2: In as yet, I can't even determine whether as is an adverb or conjunction; so I don't know where to start on OED's entry on as. Which OED definition of as matches? Please identify.
Afterword to user 'rogermue' 's answer: Idioms can defy the principle of compositionality, but Wikipedia attests to success in interpreting prepositions separately in some syntagma.
So even if as yet is an idiom, I wish to persevere to dig deeper.