Alternativ zur Option `bibliography=totocnumbered` funktioniert es auch mit `\defbibheading`
\begin{filecontents}{Literaturverzeichnis.bib}
@Book{Goossens1994,
author = {Goossens, Michel and Mittelbach,
Frank and Samarin, Alexander},
title = {The LaTeX Companion},
publisher = {Addison-Wesley},
location = {Reading, Mass.},
year = {1994},
}
\end{filecontents}
\documentclass[12pt]{scrreprt}
\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}
\usepackage[ngerman]{babel}
% Literaturverzeichnis & Co. -----------------------------------------------------------------------
\usepackage{csquotes}
\usepackage[style=apa,sortcites=true,sorting=nyt,backend=biber,bibstyle=numeric]{biblatex}
\DeclareLanguageMapping{german}{german-apa}
\bibliography{Literaturverzeichnis}
\usepackage{blindtext}
\defbibheading{lit}{\chapter{Literatur}}
\defbibheading{bibliography}{\chapter{Literatur}}
\begin{document}
\chapter{Kapitel Eins}
\blindtext
\Textcite{Goossens1994}
\printbibliography[heading=lit]
\printbibliography
\end{document}
