Let's have (for example) the following aux_dir for latexmk

# .latexmkrc
$aux_dir = ".aux";

Diagnostics for unused labels are displayed, but other diagnostics (such as Overfull \hbox) are not. If the $aux_dir is not customized, everything works.

Info about my setup:

• editor: neovim
• compilation of latex: latexmk via vimtex plugin
• setup of texlab: via nvim-lspconfig

Minimal reproducible example

\documentclass[a4paper,12pt]{article}

\usepackage{graphicx}

\overfullrule=1mm

\begin{document}

\section{Working example}

\begin{figure}[!ht]
    \centering
    \includegraphics[width=1.2\linewidth]{example-image-a}
    \caption{This is an example image.}
    \label{fig:missing}
\end{figure}

\end{document}