Autosummary should respect `:meta public:` and `:meta private:`

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

Currently autodoc allows inserting :meta private: as a way to declare a function private: https://www.sphinx-doc.org/en/master/usage/extensions/autodoc.html

However, autosummary does not do so.

Describe the solution you'd like

In autosummary, functions currently:

List containing names of “public” functions in the module. Here, “public” here means that the name does not start with an underscore. Only available for modules.

If the bold part can be changed to does not start with an underscore and does not have :meta: private, the issue should be resolved.

Describe alternatives you've considered

Customize the autosummary template to exclude each single function that I would like to exclude. Quite tedious though.

Start by tracing how autosummary builds the module functions list and how autodoc processes :meta public: and :meta private:. Update the public-function selection so metadata is respected, then add or run focused autosummary and autodoc tests covering both metadata forms and verify the generated listing.