Your question is not very clear to me.
For the its first version you can consider my comment or use the following solution:
documentclass[tikz, margin=3mm]{standalone}
\usetikzlibrary{backgrounds}
\tikzstyle{mycircle}=[draw, circle, minimum height=2.5mm]
\tikzstyle{mygreen}=[draw=green!80!black,fill=green!80!black!20!white]
\begin{document}
\begin{tikzpicture}
\node (V=) [mycircle, mygreen] at (4, 0) (V0) {};
\node (V1) [mycircle, mygreen] at (6.5, 1) {};
\node (V2) [mycircle, mygreen] at (9.25, 0) {};
\scoped[on background layer]
{
\draw[red!10, line width=2.5em, line join=round] (V0.center) -- (V2.center) -- (V1.center) -- cycle;
\fill[red!25] (V0.center) -- (V2.center) -- (V1.center) -- cycle;
}
\end{tikzpicture}
\end{document}

For the second version, if I understood you correctly, the solution can be:
\documentclass[tikz, margin=3mm]{standalone}
\usetikzlibrary{backgrounds}
\begin{document}
\begin{tikzpicture}[
mycircle/.style = {draw, circle, minimum size=2.5mm}
mygreen/.style = {draw=green!80!black,fill=green!80!black!20!white}
]
\node (V=) [mycircle, mygreen] at (4, 0) (V0) {};
\node (V1) [mycircle, mygreen] at (6.5, 1) {};
\node (V2) [mycircle, mygreen] at (9.25, 0) {};
\scoped[on background layer]
\filldraw[red!25, line width=2.5em, line join=round] (V0.center) -- (V2.center) -- (V1.center) -- cycle;
\end{tikzpicture}
\end{document}

Note: function of opacity
is to make fill (or line) transparent, i.e. that the drawing behind it is visible. Due to this in your example part of fill, which color area between zero width lines between nodes, cover inner half part of real line. Consequently, covered part of line is visible through the fill.
To have line and fill the same color, the color of the fill should not be transparent. To have fill more brighter, change the fill color, for example from red!25
to red!0
.
Addendum (off topic):
For exercise, how to make code for above MWE shorter:
\documentclass[tikz, margin=3mm]{standalone}
\begin{document}
\begin{tikzpicture}[
mycircle/.style args = {#1/#2}{circle,
draw=#1, semithick, fill=#2,
minimum size=2.5mm},
mycircle/.default = green!80!black/green!80!black!20!white
]
\begin{scope}[nodes=mycircle]
\filldraw[red!10, line width=5mm, line join=round]
(0.00,0) node {} --
(2.50,1) node {} --
(5.25,0) node {} -- cycle;
\end{scope}
\end{tikzpicture}
\end{document}
Result is the same as before.
\filldraw
instruction. Try to increase line width to3em
. – Zarko Jul 3 '20 at 10:01