Eagerly import self_outdated_check when modifying pip

The self_outdated_check module should be loaded *before* pip is replaced
as otherwise the module is liable to blow up if there are any
incompatibities between the self_outdated_check from new pip and the old
pip already loaded.

Author: ichard26

news/12675.bugfix.rst

@@ -0,0 +1,2 @@
+Eagerly import the self version check logic to avoid crashes while upgrading
+or downgrading pip at the same time.

src/pip/_internal/commands/install.py

@@ -406,6 +406,12 @@ def run(self, options: Values, args: List[str]) -> int:
                 # If we're not replacing an already installed pip,
                 # we're not modifying it.
                 modifying_pip = pip_req.satisfied_by is None
+                if modifying_pip:
+                    # Eagerly import this module to avoid crashes. Otherwise, this
+                    # module would be imported *after* pip was replaced, resulting in
+                    # crashes if the new self_outdated_check module was incompatible
+                    # with the rest of pip that's already imported.
+                    import pip._internal.self_outdated_check  # noqa: F401
             protect_pip_from_modification_on_windows(modifying_pip=modifying_pip)
 
             reqs_to_build = [