As far as I can see, you problem is not that hyphenation and hyphenation pattern in general doesdo not work properly. Your overall problem is that generally words containing hyphens cannot be hyphenated elsewhere (see e.g. Adequate hyphenation of words already containing a hyphen) and specifically your problem is that the babel-german solution "= does not quite work with biblatex (as also documented in your earlier question babelshorthand "= does not work with BibLaTeX?).
It might be instructive to briefly discuss why "= does not work. "= relies on " being a shorthand/an active character and thus ultimately on category codes. At least for me, catcodes are one of the more tricky aspects of TeX programming. Essentially (but quite possibly not entirely correctly) TeX remembers the category code of each character it encounters. That category code is essentially frozen and cannot be changed after it has been read. So the category code settings at the point when code is "read" for the first time is relevant for how it behaves later on even if the category code of the characters involved are later changed.
biblatex reads the contents of your bibliography items from the .bbl file at \begin{document}. This is done so that all data is available throughout the whole document. Crucially the file is read before babel selects the document language. In particular even if your document language is ngerman, where " is an active character/shorthand. The, the .bbl file is read at a time when " is still a normal character and not at all a shorthand.
As Ulrike Fischer pointed out in the comments, biblatex provides the command \hyphen as a replacement for "= that does not rely on (non-standard) category codes and thus works out of the box with all language settings.
\documentclass[english,ngerman]{scrartcl} \usepackage[style=numeric]{biblatex} \usepackage{babel} \usepackage{csquotes} \usepackage{dtk-logos} \begin{filecontents}{\jobname.bib} @Manual{class:scrguide, title = {KOMA-Script}, author = {Kohm, Markus}, month = May, year = 2016, url = {http://www.komascript.de/~mkohm/scrguide.pdf}, langid = {ngerman}, note = {Bestandteil der Online\hyphen Dokumentation von \TeXLive, Datei \url{scrguide.pdf}}, keywords = {manual}, } @Book{voss21:wissenschaftliche-arbeit-mit-latex, author = {Voss, Herbert}, title = {Die wissenschaftliche Arbeit mit \LaTeX}, indextitle = {Wissenschaftliche Arbeit mit LaTeX, die}, year = 2021, month = 6, subtitle = {unter Verwendung von \LuaTeX{}, KOMA\hyphen Script und Biber/\BibLaTeX{} und anderem mehr mehr}, series = {DANTE\hyphen Edition}, langid = {ngerman}, location = {Berlin}, keywords = {book}, pagetotal = 448, edition = 2, isbn = {978-3-96543-217-8}, } \end{filecontents} \addbibresource{\jobname.bib} \shorthandon{"} \begin{document} Der Eintrag~\cite{class:scrguide,voss21:wissenschaftliche-arbeit-mit-latex} aus meiner Literatur"=Datenbank erscheint im Quellen"=Verzeichnis leider mit einem \verb|"=| in der Ausgabe. \printbibliography \end{document} Note that biblatex's \hyphen is defined as \nobreak-\nobreak\hskip\z@skip and so pretty much ends up doing what David Carlisle suggested in the comments.
