\documentclass[tikz, border=5mm]{standalone}
\usepackage{tikz}
\usetikzlibrary{tikzphysics.surface}

\begin{document}

%% Test 1: place dots INSIDE the node's options via label (same scope)
\begin{tikzpicture}
  \node[wedge, wedge angle=30, wedge width=4,
        label={[inner sep=0]center:inside-test}]
    (W) at (0,0) {};

  %% also test: anchor access from OUTSIDE the node
  \fill[red] (W.bl)        circle (2pt);
  \fill[red] (W.br)        circle (2pt);
  \fill[red] (W.top)       circle (2pt);
  \fill[blue] (W.slope-mid) circle (2pt);
  \fill[blue] (W.centroid)  circle (2pt);
\end{tikzpicture}

\end{document}
