Add type annotations

A few code are revised because the type checker (mypy) doesn't allow
changing types on a variable.

PR #20935.

.github/workflows/ci_python.yaml

@@ -53,7 +53,7 @@ jobs:
           python-version: '3.7'
 
       - name: Install tools (search engine)
-        run: pip install bandit pycodestyle pyflakes
+        run: pip install bandit mypy pycodestyle pyflakes pyright
 
       - name: Gather files (search engine)
         run: |
@@ -61,6 +61,16 @@ jobs:
           echo $PY_FILES
           echo "PY_FILES=$PY_FILES" >> "$GITHUB_ENV"
 
+      - name: Check typings  (search engine)
+        run: |
+          MYPYPATH="src/searchengine/nova3" \
+          mypy \
+            --follow-imports skip \
+            --strict \
+            $PY_FILES
+          pyright \
+            $PY_FILES
+
       - name: Lint code (search engine)
         run: |
           pyflakes $PY_FILES