Change chocolatey system test to ensure uv uses the right python (#17533)

Fix #17524.

This adds a couple of new options to `scripts/check_system_python.py` to verify that it is running with the right interpreter version and that it would hopefully be the interpreter picked up by uv (although that isn't strictly necessary as other tests should fail in that case).

Additionally, since the path to the newly installed chocolatey python is not loaded from registry on every step, we now manually load it.

Beware, this will break `GITHUB_PATH` but this job wasn't using it at the moment.

scripts/check_system_python.py

@@ -52,6 +52,17 @@ if __name__ == "__main__":
         required=False,
         help="Set if the system Python version must be explicitly specified, e.g., for prereleases.",
     )
+    parser.add_argument(
+        "--check-python-version",
+        required=False,
+        help="Verify that this tool has been started with the specified python version. Omitting the patch number will match any patch number.",
+    )
+    parser.add_argument(
+        "--check-path",
+        required=False,
+        action="store_true",
+        help="Attempt to verify that the PATH is set up so that this tool's python will match the python version that uv would automatically pick up.",
+    )
     args = parser.parse_args()
 
     uv: str = os.path.abspath(args.uv) if args.uv else "uv"
@@ -60,6 +71,29 @@ if __name__ == "__main__":
     )
     python = ["--python", args.python] if args.python else []
 
+    if args.check_python_version:
+        version = ".".join(map(str, sys.version_info[:3]))
+        if args.check_python_version != version and not version.startswith(
+            args.check_python_version + "."
+        ):
+            raise Exception(
+                f"Expected to be running {args.check_python_version} but we are on {version}."
+            )
+
+    if args.check_path:
+        process = subprocess.run(
+            ["python", "-c", "import sys; print(sys.executable)"],
+            check=True,
+            stdout=subprocess.PIPE,
+        )
+        system_python_path = os.path.normcase(os.path.normpath(process.stdout))
+        our_python_path = os.path.normcase(os.path.normpath(sys.executable))
+
+        if our_python_path != system_python_path:
+            raise Exception(
+                f"Script was ran with {our_python_path} but `python` resolves to {system_python_path}"
+            )
+
     # Create a temporary directory.
     with tempfile.TemporaryDirectory() as temp_dir:
         # Ensure that the package (`pylint`) isn't installed.