chore: apply ty checks on api code with script and ci action (#24653)

web/.husky/pre-commit

@@ -41,6 +41,15 @@ if $api_modified; then
       echo "Please run 'dev/reformat' to fix the fixable linting errors."
       exit 1
     fi
+
+    # run ty checks
+    uv run --directory api --dev ty check || status=$?
+    status=${status:-0}
+    if [ $status -ne 0 ]; then
+      echo "ty type checker on api module error, exit code: $status"
+      echo "Please run 'dev/ty-check' to check the type errors."
+      exit 1
+    fi
 fi
 
 if $web_modified; then