I went back through and checked my premises.
From Elliot’s grammar article under Grouping:
Note: A phrase can be a single word. It’s not wrong, and sometimes convenient, to say that the subject of a sentence is always a “noun phrase” (a phrase which functions as a noun) because there’s nothing wrong with groups with only one thing in them.
So I understood “phrase” here as “noun” OR “noun phrase” which is why I couldn’t differentiate between “after” as a preposition or conjunction.
I looked for some other articles.
Conjunctions vs Prepositions
There are some words that can be both conjunctions and prepositions. There are certain subordinating conjunctions which are also prepositions. Some such examples are: before, after, until, since etc.
If the word is followed by a dependent or subordinating clause then it is a conjunction. If the following words are objects, nouns or pronouns then it will be a preposition.
This article is the only source I’ve found that specifically talks about how to deal with words that can operate as both prepositions and conjunctions and gives an objective way of differentiating between them. So for now I’m going to take it as the best way of making the distinction.
Going back to the original exercise.
So in this case, as “after” just joins “work” and not any sort of clause, then it is a preposition.
I don’t think it actually makes any difference in terms of meaning and understanding sentences. Preposition seems like a subset of subordinating conjunction in these cases. But it’s better to have some clear way of arbitrating this ambiguity.