\documentclass[]{article}
\usepackage[utf8x]{inputenc}
\usepackage[english]{babel}
\usepackage[T1]{fontenc}
\usepackage{amsmath,amsthm,amsfonts,amssymb}
\usepackage{graphicx}
\usepackage{floatrow}
\usepackage{subfig}
\usepackage{microtype}
\usepackage{braket}
\usepackage{physics}
\usepackage{bm}
\usepackage{scalefnt}
\usepackage{asymptote}
\usepackage{asypictureB}
\usepackage{float}
\usepackage{makecell}
\usepackage[all,cmtip]{xy}
\usepackage{thmtools,thm-restate}
\usepackage[shortlabels]{enumitem}
\usepackage{xcolor,colortbl}
\makeatletter
\def\l@subsubsection#1#2{}
\makeatother
\usepackage{tikz}
\usetikzlibrary{calc}
\usepackage{zref-savepos}
\usepackage{tabu}
\newcommand*\circled[1]{\tikz[baseline=(char.base)]{% <---- BEWARE
\node[shape=circle,draw,inner sep=2pt] (char) {#1};}}
\begin{document}
\begin{table}[H]
\centering
\begin{tabular}{c|c|c}
\circled{A}
& \circled{B}
& \circled{C}
\\ \hline
\cellcolor{red!25}{p$_1$} & \cellcolor{red!25}{p$_1$} & \cellcolor{red!25}{p$_1$} \\ \hline
\cellcolor{red!25}{p$_2$}& \cellcolor{red!25}{p$_2$} & \cellcolor{red!25}{p$_2$} \\ \hline
\cellcolor{red!25}{p$_3$} &
\cellcolor{red!25}{p$_3$} & \cellcolor{red!25}{p$_3$}
\end{tabular}
\end{table}
\end{document}
The above code creates the following table.
Is it possible to make the cell coloring not merge with the neighboring cells such that the text in the cell has the colored background but there is still some white spacing between the neighboring cells in both vertical and horizontal directions?