fix: resolve pyright type errors in api.py and test_api.py

Cast Die.code (_ExitCode) to int before passing to BottleError — Die
always holds an int but SystemExit.code is typed as str|int|None in
typeshed. Replace untyped lambda with str() as identity for
_uniquify_label_headless mock (fixes reportUnknownLambdaType).

Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>

tests/unit/test_api.py

@@ -56,7 +56,7 @@ class TestStartHeadless(unittest.TestCase):
             "bot_bottle.api._launch_bottle", return_value=("implementer-abc12", 0)
         ).start()
         patch(
-            "bot_bottle.api._uniquify_label_headless", side_effect=lambda lbl: lbl
+            "bot_bottle.api._uniquify_label_headless", side_effect=str
         ).start()
         self.addCleanup(patch.stopall)