HTML and LaTeX/PDF generation require incompatible uses of DeclareMathOperator*

Describe the bug

For Sphinx LaTeX/PDF generation to work correctly, I need to the following in my conf.py file:

# Additional stuff for the LaTeX preamble.
'preamble': """\\DeclareMathOperator*{\\argmin}{argmin}
\\DeclareMathOperator*{\\argmax}{argmax}
\\sphinxDUC{2610}{$\square$}
"""

For Sphinx HTML generation to work correctly, I need to put the \DeclareMathOperator inside the individual .. math:: pieces. For example,

.. math::
   \DeclareMathOperator*{\argmin}{argmin}
   {\bf p}^\ast &= \argmin_{{\bf p} \in \mathbb{R}^n} \; c({\bf p}) \\
   \text{such that} \; 0 &\leq v({\bf p}) \leq V \\
                       0 &\leq p_i \leq 1, \; i = 1, \ldots n

If I generate LaTeX using sphinx-build using the HTML configuration (i.e., with \DeclareMathOperator inside the individual .. math:: pieces, I see errors like this when I run latex via make.

$ make
latexmk -pdf -dvi- -ps-  'LiDO.tex'
Rc files read:
  /etc/latexmkrc
  latexmkrc
Latexmk: This is Latexmk, John Collins, 4 Apr. 2023. Version 4.80.
No existing .aux file, so I'll make a simple one, and require run of *latex.
Latexmk: applying rule 'pdflatex'...
Rule 'pdflatex':  Reasons for rerun
Category 'other':
  Rerun of 'pdflatex' forced or previously required

------------
Run number 1 of rule 'pdflatex'
------------
------------
Running 'pdflatex   -recorder  "LiDO.tex"'
------------
This is pdfTeX, Version 3.141592653-2.6-1.40.22 (TeX Live 2021/CVE-2023-32700 patched) (preloaded format=pdflatex)
 restricted \write18 enabled.
... numerous lines deleted...
! LaTeX Error: Can be used only in preamble.

See the LaTeX manual or LaTeX Companion for explanation.
Type  H <return>  for immediate help.
 ...                                              
                                                  
l.887 ...        &l_n \leq p_n \leq u_n\end{split}
                                                  
? x

The key line is the !LaTeX Error: Can be used only in preamble.

The generated LaTeX behind this error looks like this:

Consider a generic optimization problem of this sort:
\begin{equation*}
\begin{split}\DeclareMathOperator*{\argmin}{argmin}
{\bf p}^\ast = \argmin_{{\bf p} \, \in \, \mathbb{R}^n} \quad &f({\bf p}) \\
\mathrm{such that} \quad &L_1 \leq g_1({\bf p}) \leq U_1 \\
                    &\cdots \\
                    &L_m \leq g_m({\bf p}) \leq U_m \\
                    &l_1 \leq p_1 \leq u_1 \\
                    &\cdots \\
                    &l_n \leq p_n \leq u_n\end{split}
\end{equation*}

I think LaTeX requires \DeclareMathOperator* to be in the preamble.

The command to invoke sphinx looks like

$ sphinx-build -q -b latex -d ${HOME}/lido/build/clang-build/src/docs/sphinx/_doctrees ${HOME}/lido/src/docs/sphinx ${HOME}/lido/build/clang-build/src/docs/sphinx/html
$ sphinx-build --version
sphinx-build 5.0.2

Ideally, I would like a single set of Sphinx inputs to be able to generate both HTML and LaTeX documentation.

How to Reproduce

Here is index.rst for a simple reproducer:

.. LiDO documentation master file, created by
   sphinx-quickstart on Thu Aug 17 08:19:29 2023.
   You can adapt this file completely to your liking, but it should at least
   contain the root `toctree` directive.

Welcome to LiDO's documentation!
================================

.. math::
   \DeclareMathOperator*{\argmin}{argmin}
   {\bf p}^\ast &= \argmin_{{\bf p} \in \mathbb{R}^n} \; c({\bf p}) \\
   \text{such that} \; 0 &\leq v({\bf p}) \leq V \\
                       0 &\leq p_i \leq 1, \; i = 1, \ldots n

Here is a corresponding conf.py:

# Configuration file for the Sphinx documentation builder.
#
# For the full list of built-in configuration values, see the documentation:
# https://www.sphinx-doc.org/en/master/usage/configuration.html

# -- Project information -----------------------------------------------------
# https://www.sphinx-doc.org/en/master/usage/configuration.html#project-information

project = 'LiDO'
copyright = '2023, Watts'
author = 'Watts'

# -- General configuration ---------------------------------------------------
# https://www.sphinx-doc.org/en/master/usage/configuration.html#general-configuration

extensions = []

templates_path = ['_templates']
exclude_patterns = ['_build', 'Thumbs.db', '.DS_Store']



# -- Options for HTML output -------------------------------------------------
# https://www.sphinx-doc.org/en/master/usage/configuration.html#options-for-html-output

html_theme = 'alabaster'
html_static_path = ['_static']

latex_elements = {
'preamble': """\\DeclareMathOperator*{\\argmin}{argmin}
"""
}

Environment Information

Platform:              linux; (Linux-6.4.6-100.fc37.x86_64-x86_64-with-glibc2.36)
Python version:        3.10.10 (main, Jul  7 2023, 14:09:08) [Clang 15.0.7 (Fedora 15.0.7-2.fc37)])
Python implementation: CPython
Sphinx version:        7.0.0
Docutils version:      0.19
Jinja2 version:        3.1.2
Pygments version:      2.13.0

Sphinx extensions

# Add any Sphinx extension module names here, as strings. They can be extensions
# coming with Sphinx (named 'sphinx.ext.*') or your custom ones.
extensions = ['sphinx.ext.autodoc', 'sphinx.ext.doctest', 'sphinx.ext.todo', 
    'sphinx.ext.mathjax', 'sphinx.ext.ifconfig', 'sphinx.ext.graphviz']

Additional context

No response