squash! gh-127432: Add CI job to cross build Python

Make use of some GHA bits used in other build jobs

.github/workflows/build.yml

@@ -523,9 +523,21 @@ jobs:
       suppressions_path: Tools/tsan/suppressions_free_threading.txt
       tsan_logs_artifact_name: tsan-logs-free-threading
 
-  with-python-build-linux:
+  cross-build-linux:
+    name: Cross build Linux
     runs-on: ubuntu-latest
+    needs: check_source
+    if: needs.check_source.outputs.run_tests == 'true'
     steps:
+      - name: Runner image version
+        run: echo "IMAGE_VERSION=${ImageVersion}" >> "$GITHUB_ENV"
+      - name: Restore config.cache
+        uses: actions/cache@v4
+        with:
+          path: config.cache
+          key: ${{ github.job }}-${{ runner.os }}-${{ env.IMAGE_VERSION }}-${{ needs.check_source.outputs.config_hash }}
+      - name: Register gcc problem matcher
+        run: echo "::add-matcher::.github/problem-matchers/gcc.json"
       - name: Set build dir
         run:
           echo "BUILD_DIR=$(realpath ${{ github.workspace }}/../build)" >> "$GITHUB_ENV"