This is a similar problem to micro-mu in Kurier font shows up as tcedilla, but with a different solution.
For mysterious reasons, Arev doesn't come with a suitable font description file for the TS1 encoding, notwithstanding that the fonts are available.
Also, the math-micro
and text-micro
options are no longer used.
Prepare a file named ts1fav.fd
in the working directory:
\ProvidesFile{ts1fav.fd}[2004/09/07 scalable font definitions for TS1/fav.]
\expandafter\ifx\csname fvs@Scale\endcsname\relax
\let\fvs@@Scale\@empty
\else
\edef\fvs@@Scale{s*[\csname fvs@Scale\endcsname]}%
\fi
\DeclareFontFamily{TS1}{fav}{}
\DeclareFontShape{TS1}{fav}{b}{n}{
<-> \fvs@@Scale fvsb8c
}{}
\DeclareFontShape{TS1}{fav}{b}{it}{
<-> \fvs@@Scale fvsbo8c
}{}
\DeclareFontShape{TS1}{fav}{m}{n}{
<-> \fvs@@Scale fvsr8c
}{}
\DeclareFontShape{TS1}{fav}{m}{it}{
<-> \fvs@@Scale fvsro8c
}{}
\DeclareFontShape{TS1}{fav}{bx}{n}{<->ssub * fav/b/n}{}
\DeclareFontShape{TS1}{fav}{bx}{it}{<->ssub * fav/b/it}{}
\DeclareFontShape{TS1}{fav}{b}{sl}{<->ssub * fav/b/it}{}
\DeclareFontShape{TS1}{fav}{bx}{sl}{<->ssub * fav/b/it}{}
\DeclareFontShape{TS1}{fav}{m}{sl}{<->ssub * fav/m/it}{}
\endinput
Now you can modify your document into
\documentclass{article}
\usepackage{arevtext,arevmath}
\usepackage{siunitx}
\sisetup{
detect-all, % not really needed for the solution
}
\DeclareSIPrefix{\micro}{%
\text{%
\fontencoding{TS1}\fontfamily{\familydefault}\upshape
\symbol{"B5}%
}%
}{-6}
\begin{document}
\qty{100}{\micro\meter}
$\qty{100}{\micro\meter}$
\end{document}

arev
font.