My advice is to use unicode-math:

\documentclass{scrreprt}
\usepackage[ngerman, english]{babel}

\usepackage{amsmath}
\usepackage[math-style=ISO]{unicode-math}
\usepackage[final]{microtype}

\usepackage[table]{xcolor}
\usepackage[
  per-mode=symbol-or-fraction,
  locale=DE,
  sticky-per
]{siunitx}

\useshorthands{"}
\addto\extrasenglish{\languageshorthands{ngerman}}

\begin{document}
$\Psi \mathup{\Psi}$
\end{document}

You can see that the default is slanted, but with \mathup you can get the upright letter.

With unicode-math you don't need amssymb. Load mathtools, if you want it, in place of amsmath before unicode-math.

Don't load commath: it is buggy.

My advice is to use unicode-math:

\documentclass{scrreprt}
\usepackage[ngerman, english]{babel}

\usepackage{amsmath}
\usepackage[math-style=ISO]{unicode-math}
\usepackage[final]{microtype}

\usepackage[table]{xcolor}
\usepackage[
  per-mode=symbol-or-fraction,
  locale=DE,
  sticky-per
]{siunitx}

\useshorthands{"}
\addto\extrasenglish{\languageshorthands{ngerman}}

\begin{document}
$\Psi \symup{\Psi}$
\end{document}

You can see that the default is slanted, but with \symup you can get the upright letter.

With unicode-math you don't need amssymb. Load mathtools, if you want it, in place of amsmath before unicode-math.

Don't load commath: it is buggy.

Note: in the previous version of the code \mathup was used, but unicode-math underwent some changes and now \symup is the command to use for this purpose.