fix: 3-minute timeout on SSE LLM streams

[bmersereau]

Summary

• Wraps runLLMStream in both POST /chat and POST /projects/:projectId/chat with a Promise.race against a 180-second timeout
• On timeout, writes { type: "error", message: "Request timed out" } SSE event followed by [DONE] and closes the connection
• Prevents stalled upstream LLM API calls from holding SSE connections open indefinitely under load

Closes #100
Closes #114
Closes #117
Closes #119

Changes

• backend/src/routes/chat.ts — STREAM_TIMEOUT_MS = 180_000, Promise.race wrapping runLLMStream, timeout-specific error message in catch
• backend/src/routes/projectChat.ts — same pattern; STREAM_TIMEOUT_MS const placed after all imports
• backend/src/lib/__tests__/sseTimeout.test.ts — static analysis tests verifying both routes use Promise.race and the timeout
• backend/tsconfig.json — exclude __tests__ from tsc build
• backend/vitest.config.ts — include filter scoping tests to src/ to exclude compiled dist/ artifacts
• backend/package.json — "test": "vitest run" script added

Test plan

• Unit tests added and passing (3/3)
• Backend build passes

[bmersereau]

PR Review

Summary

Wraps runLLMStream in both POST /chat and POST /projects/:projectId/chat with a 180-second Promise.race timeout. On timeout the handler writes a typed error SSE event and [DONE] before closing the connection. Three static-analysis tests verify both routes use Promise.race and the timeout constant.

Findings

• [severity:praise] clearTimeout(timerId!) called on the happy path — prevents timer leak after successful stream
• [severity:praise] STREAM_TIMEOUT_MS = 180_000 is placed correctly after all imports in projectChat.ts ✓ (issue #119 resolved)
• [severity:praise] vi.mock hoisting pattern not applicable here; STREAM_TIMEOUT_MS placement verified
• [severity:nit] The timerId! non-null assertion is needed because TypeScript can't prove timerId is assigned in the Promise constructor. This is a known unavoidable pattern; no change needed

Specific checks

• "test": "vitest run" in package.json ✓
• vitest.config.ts include filter present ✓
• STREAM_TIMEOUT_MS after all imports in projectChat.ts ✓ (issue #119)
• Tests pass: 3/3 ✓

Verdict

Approve — clean.