Deprecate .egg in the imporlib-metadata backend

This provides us a path to remove all pkg_resources usages on Python
3.11 or later, and thus avoid the problem that pkg_resources uses
Python API deprecated in 3.12.

news/11996.process.rst

@@ -0,0 +1 @@
+Deprecate support for eggs for Python 3.11 or later, when the new ``importlib.metadata`` backend is used to load distribution metadata. This only affects the egg *distribution format* (with the ``.egg`` extension); distributions using the ``.egg-info`` *metadata format* (but are not actually eggs) are not affected. For more information about eggs, see `relevant section in the setuptools documentation <https://setuptools.pypa.io/en/stable/deprecated/python_eggs.html>`__.

src/pip/_internal/metadata/importlib/_envs.py

@@ -151,7 +151,7 @@ def _emit_egg_deprecation(location: Optional[str]) -> None:
     deprecated(
         reason=f"Loading egg at {location} is deprecated.",
         replacement="to use pip for package installation.",
-        gone_in=None,
+        gone_in="23.3",
     )
 
 
@@ -174,7 +174,7 @@ def _iter_distributions(self) -> Iterator[BaseDistribution]:
         for location in self._paths:
             yield from finder.find(location)
             for dist in finder.find_eggs(location):
-                # _emit_egg_deprecation(dist.location)  # TODO: Enable this.
+                _emit_egg_deprecation(dist.location)
                 yield dist
             # This must go last because that's how pkg_resources tie-breaks.
             yield from finder.find_linked(location)