I have recreated the new \nmid using your starting \bigm\vert with a \nnmid inserted into a macro that exactly simulates the "not dividing" larger symbol and it aligns perfectly with your \bigm\vert. I hope that I have answered your question.
\documentclass[a4paper,12pt]{article}
\usepackage{amsmath,amssymb}
\usepackage{graphicx}
\newcommand{\nnmid}{\bigm\vert\kern-1.5ex\raisebox{.4ex}{\rotatebox[origin=c]{40}{--}}}
\begin{document}
[a\nmid b \nnmid d\bigm\vert c]
\end{document}

You can choose also this MWE where the minus sign it is more tickness.
\documentclass[a4paper,12pt]{article}
\usepackage{amsmath,amssymb}
\usepackage{graphicx}
\newcommand{\nnmid}{\bigm\vert\kern-2.2ex\raisebox{.4ex}{\rotatebox[origin=c]{40}{$-$}}}
\begin{document}
[a\nmid b \nnmid d\bigm\vert c]
\end{document}

mathchoice. – user202729 Oct 09 '22 at 04:57