How does the verse about Allah teaching Adam the names express His wisdom in tasking humanity with worship on Earth, and how is it a reprimand to the angels for their objection?

This is an answer to your question regarding the verse: "And He taught Adam all the names" (Quran 2:31).

The established interpretations of the verse "And He taught Adam all the names" are sound, and there is no reason to reject them. The verses are explicit that Allah taught Adam the names of all things, then presented them to the angels, who were unable to identify them. Then, He commanded Adam to inform them of these names. This demonstrates that Allah appointed Adam as His vicegerent due to his knowledge, which the angels did not possess.

The correct interpretation of the Quran is indeed what is found in the well-known books of Tafsir. These interpretations are based on the understanding of the early Muslims (Salaf) and the prominent exegetes, and they are consistent with the linguistic rules of Arabic and the overall context of the Quran. Therefore, there is no valid reason to question or reject these established interpretations.