This is not a general answer to the title question, because the "determinative" (in Cambridge GEL terminology; or "determiner" in Comprehensive GEL terminology) word class seems to be heterogeneous and have a number of significant subdivisions.
"Many" can be classified as a quantifier or with the term you use in your question, "post-determiner" (which I found explained more in the blog post "Exploring determiners").
In the specific case of "These many awful photographs", I would say many does not function syntactically as a "determiner" (in Cambridge GEL terminology; or "determinative" in Comprehensive GEL terminology); rather, it is adjectival.
I did find a statement that supports this in "Chapter 2: Categories" of A Grammar of English Gelderen 2000, which says
Finally, quantifiers are adjectival, as in the many problems and in (34) [...]
- The challenges are many/few.
However, I don't know if this is a simplification, so I might be wrong about this.
It essentially means the same thing as "numerous," another word that can be a quantifier, but that clearly has adjective morphology (the suffix -ous) and that seems to also be able to be used as an adjective. As evidence that the word many can be adjectival when it comes in this post-determiner position, consider its coordination with adjectives in phrases like "these many and complex causes" or "these many and great dangers". According to "Beyond Syntactic Change: various and numerous" by Tine Breban, there is a claim made by Bache (1978) that coordination between adnominal modifiers is only possible if they have the same grammatical function.
Of course, in your example, there is no coordination, so this argument, if correct, would only show that "many" could be adjectival in this position, not that it has to be.
If it is adjectival, it would indeed be an adjunct according to the theories of grammar that I am familar with. The blog post "Of adjectives and adjuncts" by Paul Hagstrom says
Adjectives are modifiers, like adverbs are. So, the way they attach is with Adjoin.
Another description of adjectives as adjuncts is available from the XTAG Project page "Adjectives".