Adverbial subordinate clause/ phrase [duplicate]

It's a prepositional phrase that adverbially modifies what ensues.

You're assuming it's one or the other, but that's a false assumption as prepositional phrases are modifying phrases, either adjectival or adverbial, and it just so happens that it's adverbial in your sentence. As such, it is both a prepositional phrase and an adverbial phrase there.

What it isn't is a subordinate clause, not adverbial or any other kind. In order to be a subordinate clause, it would have to contain a verb. It doesn't, so it's not.

For further information, you may refer to the following link and scroll down to the heading "Understand what prepositional phrases do in a sentence":

https://www.chompchomp.com/terms/prepositionalphrase.htm

After March 2023, life will be back to normal.

It's important to distinguish category and function.

"After" is a preposition so "after March 2023" can only belong to the category preposition phrase.

The PP is functioning as a modifier in clause structure, more specifically an adjunct, so we have:

Category: preposition phrase

Function: modifier (adjunct of time)

The same applies to your other example.

Note that the head word in a phrase determines its phrasal category (preposition phrase, adjective phrase, adverb phrase and so on).