Sample demo.tex file that has tikzpicture within a equation
% Created 2022-10-14 Fri 14:48
% Intended LaTeX compiler: pdflatex
\documentclass[11pt]{article}
\usepackage[latin1]{inputenc}
\usepackage[T1]{fontenc}
\usepackage{graphicx}
\usepackage{longtable}
\usepackage{wrapfig}
\usepackage{rotating}
\usepackage[normalem]{ulem}
\usepackage{amsmath}
\usepackage{amssymb}
\usepackage{capt-of}
\usepackage{hyperref}
\usepackage{tikz}
\date{\today}
\title{}
\hypersetup{
pdftitle={},
pdfkeywords={},
pdfsubject={},
pdfcreator={Emacs 29.0.50 (Org mode 9.5.5)},
pdflang={English}}
\begin{document}
\tableofcontents
\begin{equation}
\begin{tikzpicture}[baseline=(current bounding box.center)]
\node {sqrt} % root
child { node {sqrt-iter}
child[sibling distance=5cm] { node{ good-enough }
child[sibling distance=2cm] { node { square } }
child[sibling distance=2cm] { node { abs } } }
child { node{ improve }
child { node { average } } } };
\end{tikzpicture}
\end{equation}
\begin{equation}
x=\sqrt{b}
\end{equation}
If \(a^2=b\) and \(b=2\), then the solution must be
either $$ a=+\sqrt{2} $$ or \[ a=-\sqrt{2} \].
\end{document}
How the above tex file is rendered

How the buffer looks like in emacs -Q
tikzpicture within equation environment gets a font-latex-math-face

Copy the following snippet to *scratch*, and do M-x eval-buffer.
(add-hook 'LaTeX-mode-hook
(defun my-LaTeX-mode-hook ()
(hi-lock-mode 1)
(highlight-regexp
(rx (seq
"\\begin{tikzpicture}"
"[" (group (one-or-more any)) "]"
(group (minimal-match (one-or-more (or any "\n"))))
"\\end{tikzpicture}"))
'hi-yellow 2)
(font-lock-flush))
t)
Visit the above demo.tex and do M-x revert-buffer. This is how it looks
tikzpicture gets its own face (which is hi-yellow)

To highlight tikzpicture in default face, change 'hi-yellow in the snippet to 'default.
When I open the .tex file, and I do C-h m I get
The major mode is LaTeX/P mode defined in tex-mode.el:
This function has :override advice: TeX-latex-mode.
This is an :override advice, which means that latex-mode isn’t
run at all, and the documentation below may be irrelevant.
I also see
TeX-latex-mode is an autoloaded interactive byte-compiled Lisp
function in latex.el.
(TeX-latex-mode)
Major mode in AUCTeX for editing LaTeX files.
See info under AUCTeX for full documentation.
I had trouble finding the relevant hook. You may have to find what hook is run in your case. See https://git.savannah.gnu.org/cgit/emacs/elpa.git/tree/latex.el?h=b91f15b3a375445985143ed1d6e41490ea62780a#n7161. As the screenshots, there is no problem with the snippet. May be our running environments are different. May be try putting it on TeX-mode-hook.
To test the snippet, you don't have to have to put it on a hook. Just add an interactive spec to my-LaTeX-mode-hook, and call the function with M-x ....
(I am not a tex user, auctex is one of the big old packages which was outside of Emacs for a long time. So, it has plenty of "hacks")