[Enhancement] Add unit tests for GatewayClient reconnect and backoff logic

What problem are you trying to solve?

GatewayClient manages the WebSocket connection lifecycle including exponential backoff reconnection, challenge/response handshake, a 15-second pending request timeout, and close-rejects-all-pending behavior. None of this is unit tested. The existing tests only mock the client at a high level. A regression in reconnect logic would break the entire app.

Where

• Source: packages/desktop/src/main/ws/gateway-client.ts
• Key functions: scheduleReconnect() (exponential backoff), pending request timeout (REQ_TIMEOUT_MS = 15_000), and the close handler that rejects all pending requests

What needs to be done

1. Create packages/desktop/test/gateway-client.test.ts
2. Extract the backoff calculation into a pure function and test it:
   • Verify exponential growth: attempt 1 → base delay, attempt 2 → 2x, etc.
   • Verify it caps at a maximum delay
3. Test pending request timeout:
   • A request that does not receive a response within 15s should reject
   • Use vi.useFakeTimers() to advance time
4. Test close-rejects-all-pending:
   • When the connection closes, all pending requests should reject with a connection error
5. Consider using mock-socket or a lightweight WS test harness for full lifecycle tests
6. Run pnpm check to verify

Why does this matter?

The WebSocket connection is the only transport between the app and the gateway. If reconnect logic breaks, the app is dead. Tests here are a safety net for the most critical transport layer.

Primary area

Settings or gateway connection