The columns simply aren't wide enough to express the constraint expansively. Thus, do switch to a more compact display form.

\documentclass[fleqn,twocolumn]{article}
\usepackage[short,nocomma]{optidef}
\DeclarePairedDelimiter\abs{\lvert}{\rvert} % abs
\usepackage{lipsum}
\begin{document}
\hrule\smallskip\noindent
before:
\begin{mini!}
{ b } { 1}{}{}
\addConstraint%
{ \abs{s} \le \sum_{ (i, j) \in \tilde{\gamma}c } b{ij} }
{ \le \mu \ , \quad }
{ \forall c \in \bar{\mathcal{C}}_\text{inner} }
\end{mini!}
\hrule\smallskip\noindent
after:
\begin{mini!}
{ b } { 1 }{}{}
\addConstraint%
{ \abs{s} \le \sum_{\mathclap{ (i, j) \in \tilde{\gamma}c }}
b{ij} \le \mu \quad
\forall\ c \in \bar{\mathcal{C}}_{\textrm{inner}} }{}{}{}
\end{mini!}
\hrule\smallskip
\lipsum
\end{document}
\documentclass[fleqn,twocolumn]{article}, how can it be said that I removed thefleqnoption? – Mico Sep 15 '23 at 16:08optidefpackage made various design choices, I'm sadly in no position to answer your question. I'm not the designer or maintainer of the package, and I have zero knowledge of why, or why not, various design choices were made. – Mico Sep 15 '23 at 16:14fleqndocument class option, that's naturally fine by me too. (Why wouldn't it be fine, right?!) As you didn't indicate in your query that thefleqnoption might be ignored, omitting the option was not something that occurred to me as something to be investigated. You also asked, specifically, "Why does removing the fleqn fix it?" [emphasis added] As to why the creator(s) of the package made certain choices (and/or possibly errors...), I'm simply in no position to address that question. – Mico Sep 15 '23 at 16:31fleqnoption would have a rather large effect. May I suggest you contact the passage's author/maintainer to ask your why-type questions? – Mico Sep 15 '23 at 17:24