Does such a table exist, and if so, could someone share a link to it?
The SZ is only for words in capitals (and I think for old spelling).
Für LaTeX-Nutzer gibt es auch die Umschreibung "a, "o, "u, bzw. "A, "O, "U (bzw. \"a, \"o, \"u, bzw. \"A, \"O, \"U)
You are also asking for a kind of official link.
Maybe Din 5007 helps a bit. That's a norm for sorting. An "ä" is either treated like an "a" (variant 1 of DIN 5007) or like an "ae" (variant 2).
For another official link I recommend the ICU project (International Components for Unicode). It basically is a database for all(?) languages/scripts and how to convert, sort and compare words to be used by computer programs.
They have a ICU Transform Demonstration which demonstrates the transform rules. For German, you can start with "Latin" as "Source 1" and "ASCII" as "Target 1". The example "Names (Variant)" is very impressive as well as it can transliterate Korean(?), Cyrillic, Greek to Latin.