\tikz with its node style coinciding outer math syle

tikzmath.tex

\documentclass[xelatex,a4j,jadriver=standard]{bxjsarticle}
\usepackage[hiragino]{zxjafont}
\usepackage{tikz}
\usepackage{zref}


\makeatletter
\zref@newlist{knmm}
\zref@newprop{knmm@mm}[0]{0}
\zref@addprop{knmm}{knmm@mm}
\newcount\kn@mm@count
\def\kn@mm@mklabel{%
  \global\advance\kn@mm@count by 1%
  \edef\kn@mm@label{kn@mm:\the\kn@mm@count}}
\newcommand\kn@detectmath{%
  \kn@mm@mklabel
  \mathchoice{\zref@setcurrent{knmm@mm}{0}\zref@labelbylist{\kn@mm@label}{knmm}}%
    {\zref@setcurrent{knmm@mm}{1}\zref@labelbylist{\kn@mm@label}{knmm}}%
    {\zref@setcurrent{knmm@mm}{2}\zref@labelbylist{\kn@mm@label}{knmm}}%
    {\zref@setcurrent{knmm@mm}{3}\zref@labelbylist{\kn@mm@label}{knmm}}}
\newcommand\kn@currentstyle{%
\ifcase\zref@extract{\kn@mm@label}{knmm@mm}
   \displaystyle
\or\textstyle
\or\scriptstyle
\or\scriptscriptstyle
\fi}
\def\recordstyle{\kn@detectmath}
\def\currentstyle{\kn@currentstyle}
\newcommand\tikzmath[2][]{\ensuremath{\recordstyle\tikz[outer math nodes,#1]{#2}}}
\makeatother
\tikzstyle{outer math nodes}=[
  nodes={execute at begin node=$\currentstyle, execute at end node=$}
]

\newcommand{\red}[1]{{\tikzmath[baseline]{\node[draw,inner sep=1pt,anchor=base]{#1}}}}

\begin{document}
\[
 a = \red{p}_{\red{p}_{\red{p}}}^{\red{p}}
\]
\end{document}