Make synopsis translatable

Thank you for building and maintaining Sphinx, it is a great project !

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Is your feature request related to a problem? Please describe.

I have been part of the python-docs-fr localization project.

I wanted to translate the pymodule index page: https://docs.python.org/fr/3/py-modindex.html

As far as I understand, this page is generated automatically by Sphinx. The synopsis are not available in any .po file.

How to make them available for translation?

I believe that having this page accessible in the same locales as the docs is pivotal in navigating the docs in the chosen locale.

Describe the solution you'd like

I would like to have access to the synopsis on this page, either in one associated po file, or in the respective modules po files.

Describe alternatives you've considered

I did try to discover how to make the changes by myself, but my understanding of the Sphinx project does not enable me to make the changes, in either a PR to the main branch of the project, or as a sphinx extension, or a sphinxcontrib package.

As far as my understanding goes, the changes needs to be made in Sphinx itself, not in sphinx-intl nor docutils.

Additional context

This question was part of https://github.com/python/python-docs-fr/issues/1705

I would be happy to work towards a solution for this feature with someone else in a pair programming setting, or to have some sort of support/mentoring to do so.