gh-127432: Add CI job to cross build Python

This is to avoid regressions in the cross building process

Author: matthewhughes934

.github/workflows/build.yml

@@ -523,6 +523,31 @@ jobs:
       suppressions_path: Tools/tsan/suppressions_free_threading.txt
       tsan_logs_artifact_name: tsan-logs-free-threading
 
+  with-python-build-linux:
+    runs-on: ubuntu-latest
+    steps:
+      - uses: actions/checkout@v4
+        with:
+          persist-credentials: false
+      - name: Install Dependencies
+        run: sudo ./.github/workflows/posix-deps-apt.sh
+      - name: Configure host build
+        run: ./configure --prefix "$PWD/../build/host-python"
+      - name: Install host Python
+        run: make -j8 install
+      - name: Run test subset with host build
+        run: |
+          "$PWD/../build/host-python/bin/python3" -m test test_sysconfig test_site test_embed
+      - name: Clean up build
+        run: make -j clean
+      - name: Configure cross build
+        run: ./configure --prefix "$PWD/../build/cross-python" --with-build-python "$PWD/../build/host-python/bin/python3"
+      - name: Install cross Python
+        run: make -j8 install
+      - name: Run test subset with host build
+        run: |
+          "$PWD/../build/cross-python/bin/python3" -m test test_sysconfig test_site test_embed
+
   # CIFuzz job based on https://google.github.io/oss-fuzz/getting-started/continuous-integration/
   cifuzz:
     name: CIFuzz