Wiktionary is not the right place to go for grammatical terminology. Sorry.
First, "adjective-based similes" is not a grammatical term, nor even a technical one,
since it's not clear what it might mean. So that's right out.
As I said in the comment, the name for the construction is "Equative", and there are two varieties, with somewhat different properties and peculiarities. The semantic ones are described in the link. But as I said there, I wasn't going to deal with the syntactic peculiarities.
So here are some. The Equative constructions connects two parallel clauses, with identical material deleted by Conjunction Reduction, so probably the right POS to assign as...as... is "correlative conjunction".
- She despises mustard. He loves ketchup.
She despises mustard as much as he loves ketchup.
She despises mustard. He despises ketchup.
- She despises mustard as much as he despises ketchup.
She despises mustard as much as he does ketchup.
She despises mustard. He despises mustard.
- She despises mustard as much as he despises mustard.
- She despises mustard as much as he does.
She despises mustard as much as he.
She hates me. She hates him.
- She hates me as much as she hates him.
- She hates me as much as she does him.
- She hates me as much as him.
So the answer about they/them, at least, is to use whatever case the NP being compared uses. If she's comparing her hate for him with her hate for me, use him; if she's comparing the way she hates something with the way he does, use he.
The problem arises when too much has been left out.
Does
- I like Bill better than Betty.
mean
- I like Bill better than I like Betty
or does it mean
- I like Bill better than Betty likes Bill ?
And what happens when you use pronouns?