\documentclass[12pt]{article}

\usepackage{fontspec}
\usepackage{polyglossia}

\usepackage{makeidx}
\makeindex

\setdefaultlanguage{german}
\setmainfont{Noto Serif}
\setsansfont{Noto Serif}

\pagestyle{empty}
\begin{document}
\thispagestyle{empty}

a\index{a}.
A\index{A}.
ad\index{ad}.
AD\index{AD}.
ae\index{ae}.
AE\index{AE}.
ä\index{ä}.
Ä\index{Ä}.
af\index{af}.
AF\index{AF}.

\printindex

\end{document}


\index{}.
