Describe the bug

Since Sphinx 5.0.0 (PR #10191) there is a mechanism for PDF output via LaTeX so that footnotes which end up on a later page get referred to as Page N, M where N is page number and M footnote number.

But sometimes the Page N, part is printed even though the footnote is on same page as footnote mark.

How to Reproduce

index.rst

Welcome to FOO's documentation!
===============================

.. toctree::

   index1
   index2

index1.rst

A chapter
=========

Test footnote in title [#]_
---------------------------

Text

.. [#] I am on same page

index2.rst

Another chapter
===============


Problematic PR [#]_
-------------------

Text.

.. [#] https://github.com/sphinx-doc/sphinx/pull/10191

Environment Information

Python version:        3.12.3 (v3.12.3:f6650f9ad7, Apr  9 2024, 08:18:48) [Clang 13.0.0 (clang-1300.0.29.30)])
Python implementation: CPython
Sphinx version:        7.4.0+/98f953e15
Docutils version:      0.21.2
Jinja2 version:        3.1.4
Pygments version:      2.18.0

Sphinx extensions

No response

Additional context

Originally reported on sphinx-users newsgroup news://news.gmane.io:119/5ce01972-b17d-407f-9b62-742ce50a7375n@googlegroups.com