It seems to be an optical effect between the 1 and 10 point font size. Exchanging 100 for 500 everything seems normal (to the eye). The same by enlarging or decreasing the size of the font. I do not know if siunitx is modifying the space between the numbers and the units. Typesetting \SI{500}{} or \SI{500}{} the middle 0 appears perfectly centered. Compare also the result when omitting SI using {100 \textmu m}.
\documentclass{article}
\usepackage{mwe}
\usepackage{tikz}
\usepackage{siunitx}
\begin{document}
default size font
\begin{tikzpicture}
\draw (0, 0)
node (image) { \includegraphics[width=1cm]{example-image} };
\draw[red, x={(image.south east)}, y={(image.north west)}] (0.5, 0.5)
node (text) {\SI{100}{\micro\meter}};
\end{tikzpicture}
\begin{tikzpicture}
\draw (0, 0)
node (image) { \includegraphics[width=1cm]{example-image} };
\draw[red, x={(image.south east)}, y={(image.north west)}] (0.5, 0.5)
node (text) {\SI{500}{\micro\meter}};
\end{tikzpicture}
without SI
\begin{tikzpicture}
\draw (0, 0)
node (image) { \includegraphics[width=1cm]{example-image} };
\draw[red, x={(image.south east)}, y={(image.north west)}] (0.5, 0.5)
node (text) {100 \textmu m };
\end{tikzpicture}
\begin{tikzpicture}
\draw (0, 0)
node (image) { \includegraphics[width=1cm]{example-image} };
\draw[red, x={(image.south east)}, y={(image.north west)}] (0.5, 0.5)
node (text) {500 \textmu m};
\end{tikzpicture}
{\large%
larger font
\begin{tikzpicture}
\draw (0, 0)
node (image) { \includegraphics[width=1cm]{example-image} };
\draw[red, x={(image.south east)}, y={(image.north west)}] (0.5, 0.5)
node (text) { \SI{100}{\micro\meter} };
\end{tikzpicture}
}
{\small%
smaller font
\begin{tikzpicture}
\draw (0, 0)
node (image) { \includegraphics[width=1cm]{example-image} };
\draw[red, x={(image.south east)}, y={(image.north west)}] (0.5, 0.5)
node (text) { \SI{100}{\micro\meter} };
\end{tikzpicture}
}
\end{document}

UPDATE
In fact, the number 1 is very different from the others (and from the letter l!) In terms of sideberarings. This is the output using the program provided by Philipp Gesang.
Accessing side-bearings in LuaTeX

The bounding boxes of the numbers are similar between them. This is the output of Yiannis Lazarides answer to
Bounding box for each letter

So the number 1 really extends to the left of the image! It is just a coincidence that at 10pt the left border of the image it is right on the ink.
draw=black,,inner sep=0ptto your text node options, You will see that all characters do not participate to the bounding box in the same fashion. Btw you obtain the same result with\node[text=red] (text) { \SI{100}{\micro\meter} };– BambOo Nov 04 '20 at 18:50----. Compile\begin{tikzpicture} \foreach \number in {1,...,9}{\draw[common] (0.5, 0.5) node[inner sep=0pt,draw=black,xshift=\number*1.75 ex,rotate=90] (text) {\number};}withtikzloaded to see some illustration of this. \end{tikzpicture} – BambOo Nov 05 '20 at 22:581character is particularly different from the other numbers – BambOo Nov 05 '20 at 22:58