Add end-to-end tests for a full agent run including tool calls

[neooriginal]

This issue is AI generated.

Problem

test/e2e/ covers only register_login_logout.test.js and qr_login.test.js. No end-to-end test simulates a full agent run: submitting a task via WebSocket, the engine selecting and executing tools, and completing with a final response. This means regressions in the engine loop, tool runner, or result streaming are only caught by unit tests that mock at a much lower level — or by manual testing.

Evidence

• test/e2e/ — two test files, neither covers agent runs.
• No test in any suite submits a real task via agent:run and waits for a run:complete event.

Required change

Add an e2e test that:

1. Registers/logs in a test user.
2. Connects a Socket.IO client.
3. Emits agent:run with a simple deterministic task (e.g. "what is 2+2" with a mock or real model).
4. Waits for run:complete and asserts the result structure.
5. Verifies tool events appeared in the correct order.

Add a second test that exercises the tool approval gate: a task that requires an approval, where the test client automatically approves via the REST API, and asserts the run completes.

Acceptance criteria

• At least one e2e test covers a full agent run from WebSocket submission to completion.
• At least one e2e test covers the tool approval handshake.
• Tests are deterministic (use a fixed simple task or a stubbed model response).
• Tests are included in npm run test:e2e.