Macron accent above some Cyrillic letters is shifted
OpenType fonts require very patient work for supporting combining characters, that's a fact, and similar problems are, unfortunately, common.
Apparently, the font developer here forgot to add proper anchor points for combining characters in some slots of the font.
Also я Е О Э Ю Я suffer from the same problem. However, this can be cured by using the legacy method for accents.
\documentclass{scrartcl}
\usepackage{polyglossia}
\usepackage{fontspec}
\setdefaultlanguage{russian}
\setmainfont{EB Garamond}
\newfontfamily\cyrillicfont{EB Garamond}
\DeclareTextCompositeCommand{\=}{TU}{ю}{\accent"0304 ю}
\DeclareTextCompositeCommand{\=}{TU}{я}{\accent"0304 я}
\DeclareTextCompositeCommand{\=}{TU}{Е}{\accent"0304 Е}
\DeclareTextCompositeCommand{\=}{TU}{О}{\accent"0304 О}
\DeclareTextCompositeCommand{\=}{TU}{Э}{\accent"0304 Э}
\DeclareTextCompositeCommand{\=}{TU}{Ю}{\accent"0304 Ю}
\DeclareTextCompositeCommand{\=}{TU}{Я}{\accent"0304 Я}
\KOMAoptions{fontsize = 14}
\begin{document}
ш\={ю}кан
\=а\=е\=и\=о\=у\=э\=ю\=я
\=A\=Е\=И\=О\=У\=Э\=Ю\=Я
\end{document}
For the record, here's the output with the seven \DeclareTextCompositeCommand
lines omitted.