Add Architecture-Specific PATH Management for Python with --user Flag on Windows (#1122)

* logic to update install oath with --user flg

* format update

* format update

* update

* test job to validate --user flag installtion

* updated the script

* updated the yaml

* update the inputs

* updated script

* update the correct script file name

* updated script and yaml

* npm run format-check

* fix-test failures

* path update

* check failure fix

* updated test

* update free threaded version

* updated the comments

.github/workflows/e2e-cache-freethreaded.yml

@@ -58,7 +58,7 @@ jobs:
             macos-latest,
             macos-13
           ]
-        python-version: [3.13.0t, 3.13.1t, 3.13.2t]
+        python-version: [3.13.1t, 3.13.2t, 3.13.5t]
     steps:
       - uses: actions/checkout@v4
       - name: Setup Python
@@ -148,7 +148,7 @@ jobs:
             macos-latest,
             macos-13
           ]
-        python-version: [3.13.0t, 3.13.1t, 3.13.2t]
+        python-version: [3.13.1t, 3.13.2t, 3.13.5t]
     steps:
       - uses: actions/checkout@v4
       - name: Setup Python

.github/workflows/e2e-tests.yml

@@ -38,7 +38,7 @@ jobs:
       - name: Verify 3.9.13
         run: python __tests__/verify-python.py 3.9.13
 
-      - name: Run with setup-python 3.9.13
+      - name: Run with setup-python 3.10.11
         uses: ./
         with:
           python-version: 3.10.11
@@ -89,6 +89,7 @@ jobs:
           python-version: '<3.13'
       - name: Verify <3.13
         run: python __tests__/verify-python.py 3.12
+
       - name: Test Raw Endpoint Access
         run: |
           curl -L https://raw.githubusercontent.com/actions/python-versions/main/versions-manifest.json | jq empty