Fix mypy type checking via creating a nox typecheck session

[notatallshaw]

This moves type checking out of the pre-commit and into a dedicated nox -s typecheck, this was inspired by and succeeds #12866.

On top of the reasons outlined there there are two big issues with pip's type checking:

1. The additional dependencies in the .pre-commit.yaml are rarely updated and currently obsolete

This PR fixes that by making the nox -s typecheck a new type-check dependency groups, which inherits from the existing test dependency group, a new docs dependency group, and a couple of other dependency groups that define various parts of pip.

Taking the changes from #12866 and apply this increased the number of mypy errors from 0 to 48.

2. Vendored dependencies that use type stubs are not currently type checked

Pip vendors libraries like requests which do not include type hints, normally this is fixed by installing a stubs package, types-requests at type hint time, however this was not being picked up by mypy because it does not recognized pip._vendor.requests as requests.

This can be fixed by doing all the imports of vendored libraries that don't include type hints like this (fortunately there are only a few libraries that need this):

if TYPE_CHECKING:
    import requests
else:
    from pip._vendor import requests

Doing this increased the number of mypy errors from 48 to 71.

The rest of the PR is simply about fixing all the type check errors, I tried to be very conservative, using # type: ignore and cast rather than making complicated refactors, but there are definitely a few bugs that were fixed in this as well.

A side benefit is pre-commit runs much much faster, allowing you to enable it locally and it not be painful.

[notatallshaw]

Ah, there's a number of issues to work through, it seems I broke a few tests, and vendoring uses an old version of toml that can not correctly parse mixed type tables. I'll have to return to this next week.