fix: address multiple code quality improvements across backend and frontend

Backend fixes:
- Fix JWT sub claim: encode as str(user.id), decode with int() cast (python-jose requirement)
- Replace all deprecated datetime.utcnow() with datetime.now(timezone.utc)
- Replace deprecated FastAPI @app.on_event() with modern lifespan context manager
- Replace deprecated Pydantic class Config with model_config = ConfigDict(...)
- Replace deprecated Pydantic .dict() with .model_dump()
- Fix overly broad except (GmailInjectionError, Exception) → except Exception
- Remove unused GmailInjectionError import
- Fix TokenPayload schema sub field type from int to str

Frontend:
- Create frontend/src/lib/api.ts — API client module with auth, user, mail accounts, processing runs APIs
- Add !frontend/src/lib/ to .gitignore negation

Tests:
- Add 3 new JWT tests (sub string encoding, access token type, refresh token type)
- Update test_token_payload_schema for string sub claim
- All 128 tests pass

Co-authored-by: christianlouis <361235+christianlouis@users.noreply.github.com>
Agent-Logs-Url: https://github.com/christianlouis/pop_puller_to_gmail/sessions/e0b13eb0-8de7-4f02-81e4-e202cbba4608

backend/tests/unit/test_schemas.py

@@ -109,8 +109,8 @@ class TestTokenSchemas:
 
     def test_token_payload_schema(self):
         """Test TokenPayload schema"""
-        payload = TokenPayload(sub=42, type="access")
-        assert payload.sub == 42
+        payload = TokenPayload(sub="42", type="access")
+        assert payload.sub == "42"
         assert payload.type == "access"
 
     def test_google_auth_request(self):