ci: add GitHub Actions workflow to test C and Python API doc generation

Introduce separate jobs to test C (Doxygen) and Python (Sphinx) API documentation generation. Ensures build failures are caught early, as API changes often produce warnings that developers miss without automated checks.

.github/workflows/main.yml

@@ -90,3 +90,31 @@ jobs:
       - name: Check spelling
         run: |
           codespell
+
+  test-c-api-docs:
+    runs-on: ubuntu-latest
+    name: Test C API Documentation Generation
+    steps:
+      - uses: actions/checkout@v4
+      - name: Install dependencies
+        run: |
+          sudo apt-get update
+          sudo apt-get install -y --no-install-recommends make doxygen
+      - name: Test C API docs generation
+        run: |
+          cd apidocs/c/
+          doxygen c-prof.conf
+
+  test-python-api-docs:
+    runs-on: ubuntu-latest
+    name: Test Python API Documentation Generation
+    steps:
+      - uses: actions/checkout@v4
+      - name: Install dependencies
+        run: |
+          sudo apt-get update
+          sudo apt-get install -y --no-install-recommends make python3-sphinx
+      - name: Test Python API docs generation
+        run: |
+          cd apidocs/python/
+          sphinx-apidoc -f -o . src && make -j$(nproc) xml SPHINXOPTS="-W --keep-going -n"