You are running into the peculiarities of biblatex's implementation of sentence casing (\MakeSentenceCase) and its brace protection against case changes. biblatex emulates (on the LaTeX side) the case changing that BibTeX applies with change.case$. biblatex's version largely copies BibTeX's behaviour, but due to its implementation, there are some differences (the most important of which are documented in the biblatex manual, pp. 253-255 in v3.14, cf. https://github.com/plk/biblatex/issues/871).
Let's have a look at the following, slightly more systematic example
\documentclass{article}
\usepackage[ngerman,main=english]{babel}
\useshorthands*{"}
\addto\extrasenglish{\languageshorthands{ngerman}}
\begin{filecontents}{\jobname.bib}
@article{Wegener85,
Author = {Heide Wegener},
Journal = {Linguistische Berichte},
Pages = {127--139},
Title = {"`Er bekommt widersprochen"'
-- Argumente Test/""Test
für die Existenz eines Dativpassivs im Deutschen},
Volume = {96},
Year = {1985},
}
@article{Wegener86,
Author = {Heide Wegener},
Journal = {Linguistische Berichte},
Pages = {127--139},
Title = {{"`Er bekommt widersprochen"'
-- Argumente Test/""Test
für die Existenz eines Dativpassivs im Deutschen}},
Volume = {96},
Year = {1986},
}
@article{Wegener87,
Author = {Heide Wegener},
Journal = {Linguistische Berichte},
Pages = {127--139},
Title = {{{"`Er bekommt widersprochen"'
-- Argumente Test/""Test
für die Existenz eines Dativpassivs im Deutschen}}},
Volume = {96},
Year = {1987},
}
@article{Wegener95,
Author = {Heide Wegener},
Journal = {Linguistische Berichte},
Pages = {127--139},
Title = {\glqq Er bekommt widersprochen"'
-- Argumente Test/""Test
für die Existenz eines Dativpassivs im Deutschen},
Volume = {96},
Year = {1995},
}
@article{Wegener96,
Author = {Heide Wegener},
Journal = {Linguistische Berichte},
Pages = {127--139},
Title = {{\glqq Er bekommt widersprochen"'
-- Argumente Test/""Test
für die Existenz eines Dativpassivs im Deutschen}},
Volume = {96},
Year = {1996},
}
@article{Wegener97,
Author = {Heide Wegener},
Journal = {Linguistische Berichte},
Pages = {127--139},
Title = {{{\glqq Er bekommt widersprochen"'
-- Argumente Test/""Test
für die Existenz eines Dativpassivs im Deutschen}}},
Volume = {96},
Year = {1997},
}
@article{Wegener05,
Author = {Heide Wegener},
Journal = {Linguistische Berichte},
Pages = {127--139},
Title = {Test "`Er bekommt widersprochen"'
-- Argumente Test/""Test
für die Existenz eines Dativpassivs im Deutschen},
Volume = {96},
Year = {2005},
}
@article{Wegener06,
Author = {Heide Wegener},
Journal = {Linguistische Berichte},
Pages = {127--139},
Title = {{Test "`Er bekommt widersprochen"'
-- Argumente Test/""Test
für die Existenz eines Dativpassivs im Deutschen}},
Volume = {96},
Year = {2006},
}
@article{Wegener07,
Author = {Heide Wegener},
Journal = {Linguistische Berichte},
Pages = {127--139},
Title = {{{Test "`Er bekommt widersprochen"'
-- Argumente Test/""Test
für die Existenz eines Dativpassivs im Deutschen}}},
Volume = {96},
Year = {2007},
}
\end{filecontents}
\usepackage[
style=langsci-unified,
% autolang=langname,
backend=biber,
]{biblatex}
\addbibresource{\jobname.bib}
\begin{document}
Test"=Sequenz "`Ergative"' Verben
\nocite{*}
\printbibliography
\end{document}

Before we start discussing the results, note that it is in general not a good idea to just protect the whole title field with a single pair of curly braces in a WYSIWYG approach
title = {{Title That Remains Unchanged}},
In English (and other languages that use sentence casing) you should only protect those words that need case protection. In case your title is in a foreign language that doesn't want sentence casing, you should tell biblatex about it with langid. (With langid = {ngerman}, or langid = {german}, there is no case change in the entry.)
That said, we'd face the same underlying issue if we had to protect the first word of the title.
With that out of the way, notice first that " and \glqq behave analogously. This is intentional. If " is active (usually because it is a babel shorthand) it will trigger the same behaviour as a control sequence in \MakeSentenceCase. I guess that is mainly in order to be able to treat "A and \"A (for Ä) the same. (The method used by biblatex to ensure that an active " is treated like a macro has the potential to break if " is used as a 'normal character' and not in its shorthand capacity.)
The main issue here is that biblatex and BibTeX's sentence casing function treats a brace group (at brace level 0) starting with a control sequence as a single character. That is to say {\"A} and {\relax Foo} are treated as a single character even though they consist of more stuff. That function allows BibTeX to correctly build first name initials with accented characters. It is also the basis of the 'multi-letter initials' trick (see BibTeX: Abbreviate first name (aka given name) to 2 or 3 letters (not 1)).
This 'a brace group starting with a control sequence is a single character' behaviour only becomes a problem in biblatex if the brace group is at the beginning of the string. Unlike BibTeX's case changer, biblatex's case changer explicitly capitalises the first character of the string. If the string starts with a brace group starting with a control sequence, then this whole group is capitalised as one character. So {\"a} becomes {\"A} (good) and {\relax Foo} becomes {\relax FOO} (hmmm...).
In
Title = {{\glqq Er bekommt widersprochen"'
-- Argumente Test/""Test
für die Existenz eines Dativpassivs im Deutschen}},
the entire title is treated as a single character. Since it is the first character in the string, it is capitalised in its entirety. So we get all-caps.
This is what the biblatex documentation tries to explain with
The first letter of its argument is capitalised with \MakeUppercase. This is
different from BibTeX's change.case$, which does not touch the first letter
of its argument. Note that a pair of braces that starts with a control sequence
will be treated as one character for capitalisation purposes. This means that
the entire argument of a command protected with a single pair of braces is
capitalised.
In your case there is an easy way out of this dilemma: Use double braces if you would otherwise end up with a single brace group starting with a control sequence.
Title = {{{\glqq Er bekommt widersprochen"'
-- Argumente Test/""Test
für die Existenz eines Dativpassivs im Deutschen}}},
It is tempting to make using double curly braces for case protection a general rule, but I'd try to resist that temptation.
Note that the next version of biblatex will feature a new case changing function based on expl3 code that does not exhibit this behaviour any more and is overall more robust. See https://github.com/plk/biblatex/issues/960 and https://github.com/plk/biblatex/pull/1005 for background and more details. In particular it will be possible to use a different case protection mechanism that does not rely on curly braces, whose meaning is overloaded too much in BibTeX, alone.
title = {{iPhone} Manual},should do it. – moewe Jun 06 '20 at 14:03