As mentioned in the comments, biblatex (and indeed BibTeX) has no concept of a middle name. Everything that is not family name, "von" part (prefix), "junior" part (suffix) is understood as given name.
It would be possible to make biblatex distinguish between first given names and middle names if we use the extended name format and add a new name part. But this requires a slightly unnatural input (cf. Bibtex/Biber: how to cite an author using Ethiopian conventions?) and in particular would not change the handling of names specified in the normal <prefix> <family>, <suffix>, <given> or <given> <prefix> <family> order in the .bib file. This solution has the advantage that Biber knows about the different name parts and can act accordingly for sorting, name uniqueness etc.
A simpler solution (with the drawback that Biber does not know about it) is to have the middle names identified and dropped on the LaTeX side after the names have been parsed. l3regex makes that fairly easy if you know about the special format biblatex uses for names (name parts are separated with \bibnamedelima, \bibnamedelimb, \bibnamedelimi and not just spaces).
\documentclass{scrreprt}
\usepackage[shorthands=off,american]{babel}
\usepackage{csquotes}
\usepackage[bibstyle=verbose, language=auto, autolang=other, dashed=true,
maxcitenames=2, sorting=nyt, alldates=year]{biblatex}
\renewcommand{\mkbibnamefamily}{\textsc}
\renewcommand{\mkbibnamegiven}{\getfirstgivenname}
\ExplSyntaxOn
\seq_new:N \l_ingmar_givennames_seq
\regex_const:Nn \c_ingmar_splitnames_regex { \c{bibnamedelim(a|b|i)}|\s+ }
\cs_new_protected_nopar:Npn __ingmar_getfirstgiven:n #1
{
\regex_split:NnN \c_ingmar_splitnames_regex { #1 } \l_ingmar_givennames_seq
\seq_item:Nn \l_ingmar_givennames_seq {1}
}
\cs_generate_variant:Nn __ingmar_getfirstgiven:n { o }
\NewDocumentCommand \getfirstgivenname {m}
{
__ingmar_getfirstgiven:o {#1}
}
\ExplSyntaxOff
\begin{filecontents}{\jobname.bib}
@article{Becker.2012,
title = {Male gender bias in autism and pediatric autoimmunity},
author = {Becker, Kevin G. and John Q. Public},
date = {2012},
journaltitle = {Autism research},
volume = {5},
number = {2},
pages = {77--83},
langid = {english},
}
@article{Bejerot.Eriksson.2014,
title = {Sexuality and gender role in autism spectrum disorder},
author = {Bejerot, Susanne Barbara Camelia and Eriksson, Jonna M.},
date = {2014},
journaltitle = {PloS one},
volume = {9},
number = {1},
pages = {111--141},
langid = {english},
}
@book{Cardon.Matson.2016,
title = {Technology and the Treatment of Children with Autism Spectrum Disorder},
editor = {Cardon, Teresa and Matson, Johnny X.},
date = {2016},
publisher = {Springer},
location = {Heidelberg and New York and Dordrecht and London},
langid = {english},
}
\end{filecontents}
\addbibresource{\jobname.bib}
\begin{document}
\nocite{*}
\printbibliography
\end{document}

You can see how that goes wrong in
\documentclass{article}
\usepackage[shorthands=off,american]{babel}
\usepackage{csquotes}
\usepackage[style=authoryear]{biblatex}
\renewcommand{\mkbibnamefamily}{\textsc}
\renewcommand{\mkbibnamegiven}{\getfirstgivenname}
\ExplSyntaxOn
\seq_new:N \l_ingmar_givennames_seq
\regex_const:Nn \c_ingmar_splitnames_regex { \c{bibnamedelim(a|b|i)}|\s+ }
\cs_new_protected_nopar:Npn __ingmar_getfirstgiven:n #1
{
\regex_split:NnN \c_ingmar_splitnames_regex { #1 } \l_ingmar_givennames_seq
\seq_item:Nn \l_ingmar_givennames_seq {1}
}
\cs_generate_variant:Nn __ingmar_getfirstgiven:n { o }
\NewDocumentCommand \getfirstgivenname {m}
{
__ingmar_getfirstgiven:o {#1}
}
\ExplSyntaxOff
\begin{filecontents}{\jobname.bib}
@book{doe:a,
title = {Book A},
author = {Jane Emilia Doe},
date = {2020},
}
@book{doe:b,
title = {Book B},
author = {Jane Edith Doe},
date = {2020},
}
\end{filecontents}
\addbibresource{\jobname.bib}
\begin{document}
\cite{doe:a,doe:b}
\printbibliography
\end{document}

The two different works appear to have the same citation label and doe:b is seemingly incorrectly sorted before doe:a.
A fusion of the two approaches would be to use a Biber sourcemap to drop the undesired middle name initials directly when the data is read. Unfortunately, such a solution would have to replicate parts of the name parsing itself, because it would have to deal with all of Jane Emilia Doe, Doe, Jane Edith, Georgina Anne de la Name Nother before they are split into their name parts.
biblatexhas no notion of a middle name. Leaving aside the "von" and "junior" parts everything that is not family name is the given name. (See also https://github.com/plk/biblatex/issues/980.) You could use the extended name format to tell Biber about given vs middle names, but that means you will have to use rather 'unnatural' input (cf. e.g. https://tex.stackexchange.com/q/313176/35864). Alternatively you could try to use some string manipulation on the LaTeX side to drop everything but the first given name. (I'd look intoexpl3regexes) – moewe Jul 28 '21 at 09:58