There are a few intersecting problems here. The first is that, when you load NewCM10, LaTeX looks for the file NewCM10.fontspec. This only declares bold and italic faces within a SizeFeatures= block, which confuses polyglossia into not being able to find the bold font. The solution to that is to copy and paste the contents of the .fontspec file, adding a fallback:
\defaultfontfeatures[NewCM10-Book]
{
Extension = .otf ,
Font = NewCM10-Book,
ItalicFont=NewCM10-BookItalic,%
BoldFont=NewCM10-Bold,%
BoldItalicFont=NewCM10-BoldItalic,%
SlantedFont=NewCM10-Book,%
BoldSlantedFont=NewCM10-Bold,%
SmallCapsFeatures={Numbers=OldStyle},
SizeFeatures={%
{Size=-8, Font=NewCM08-Book,
ItalicFont=NewCM08-BookItalic,%
BoldFont=NewCM10-Bold,%
BoldItalicFont=NewCM10-BoldItalic,%
SlantedFont=NewCM08-Book,%
BoldSlantedFont=NewCM10-Bold,%
SmallCapsFeatures={Numbers=OldStyle}},
{Size=8, Font=NewCM08-Book,
ItalicFont=NewCM08-BookItalic,%
BoldFont=NewCM10-Bold,%
BoldItalicFont=NewCM10-BoldItalic,%
SlantedFont=NewCM08-Book,%
BoldSlantedFont=NewCM10-Bold,%
SmallCapsFeatures={Numbers=OldStyle}},
{Size= 9-, Font = NewCM10-Book,
ItalicFont=NewCM10-BookItalic,%
BoldFont=NewCM10-Bold,%
BoldItalicFont=NewCM10-BoldItalic,%
SlantedFont=NewCM10-Book,%
BoldSlantedFont=NewCM10-Bold,%
SmallCapsFeatures={Numbers=OldStyle}}%
}}
Having done that, you can now load the font as your main font:
\setmainfont{NewCM10-Book} % Ligatures: bei newfontface definiert
The font does provide Language=German, but it is broken. You could therefore also load,
\newfontfamily\germanfont{NewCM10-Book}[Language=German]
But, if you do this, the font file does not enable the small-caps feature with Language=German, so it will simply break. With Language=Default, the \textsc command will follow traditional orthography, rather than giving you a Großes Eszett.
This, inclidentally, means that someone using babel to set New Computer Modern as the German font needs to, in addition to the extra setup above, override the automatic language selection with something like \babelfont[german]{rm}[Language=Default]{NewCM10-Book}.
The MWE
\documentclass{scrartcl}
\usepackage{polyglossia}
\setdefaultlanguage[babelshorthands]{german}
\setotherlanguage[variant=british]{english}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Font
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\defaultfontfeatures[NewCM10-Book]
{
Extension = .otf ,
Font = NewCM10-Book,
ItalicFont=NewCM10-BookItalic,%
BoldFont=NewCM10-Bold,%
BoldItalicFont=NewCM10-BoldItalic,%
SlantedFont=NewCM10-Book,%
BoldSlantedFont=NewCM10-Bold,%
SmallCapsFeatures={Numbers=OldStyle},
SizeFeatures={%
{Size=-8, Font=NewCM08-Book,
ItalicFont=NewCM08-BookItalic,%
BoldFont=NewCM10-Bold,%
BoldItalicFont=NewCM10-BoldItalic,%
SlantedFont=NewCM08-Book,%
BoldSlantedFont=NewCM10-Bold,%
SmallCapsFeatures={Numbers=OldStyle}},
{Size=8, Font=NewCM08-Book,
ItalicFont=NewCM08-BookItalic,%
BoldFont=NewCM10-Bold,%
BoldItalicFont=NewCM10-BoldItalic,%
SlantedFont=NewCM08-Book,%
BoldSlantedFont=NewCM10-Bold,%
SmallCapsFeatures={Numbers=OldStyle}},
{Size= 9-, Font = NewCM10-Book,
ItalicFont=NewCM10-BookItalic,%
BoldFont=NewCM10-Bold,%
BoldItalicFont=NewCM10-BoldItalic,%
SlantedFont=NewCM10-Book,%
BoldSlantedFont=NewCM10-Bold,%
SmallCapsFeatures={Numbers=OldStyle}}%
}}
\setmainfont{NewCM10-Book} % Ligatures: bei newfontface definiert
\begin{document}
\noindent\textbf{\textsc{Frauenfußball}} \
\textsc{Frauenfußball} \
\textbf{Frauenfußball}
\end{document}

if you also want this to work for sans-serif and monospace, you need to do something similar with NewCMMono10-Book and NewCMSans10-Book.
What if you really want the Großes Eszett? If you don’t want to be pragmatic and switch to some other font that makes this substitution, I did write some code back in 2020 that could be adapted to capitalize using the de-alt rules and rescale to get an \ersatzsc command.
optexto the file:\fontfam[newcm] \caps\bf Text. \bye– wipet Mar 13 '22 at 17:03\setmainfont{NewCM10-Book.otf}then\newfontface\germanfont{NewCM10-Book.otf}[...]? The two setups include almost the exact sameScript,LanguageandLigaturessettings (btw, you probably wantLigatures={Common,TeX}). A single\setmainfont{NewCM10-Book.otf}[ItalicFont=...,BoldFont=...,...]should work. You probably also needSmallCapsFeatures={Letters=SmallCaps,Numbers=OldStyle}. – Ruixi Zhang Mar 13 '22 at 17:54\newfontface\germanfont{…}because of a bug previously. The ligatures were not working for german if I was usingpolyglossia. But I'll try that.My previous question: https://tex.stackexchange.com/questions/631464/fontspec-and-polyglossia-in-german-turns-off-ligatures-in-ncm-newcomputermodern
– Martin Dagleish Mar 13 '22 at 18:57Ligatures=Common, or a separate\germanfont. By default,fontspec(and thereforepolyglossia) addsLigatures=Commonto\setmainfontand\setsandfont. – Davislor Mar 13 '22 at 22:48