test: repair route harness error rendering + stop AI-checker spawning real processes in tests (#97)

* fix(test): share route error handler with test harness + fix stale assertions

The route test harness built a bare Fastify instance without the production
global error handler (server.ts), so structured errors thrown by route helpers
(findSessionOrFail → 404, parseBody → 400) fell through to Fastify's default
handler — yielding a `{statusCode,error,message}` body instead of the
`{success:false,...}` shape, and the tests asserted the old implicit-200
behavior. 51 route tests across 7 files were red.

- Extract the handler into src/web/route-error-handler.ts; server.ts and the
  test harness now install the identical handler (single source of truth).
- Correct stale assertions across route test files: throw-based error paths
  now assert 404 (unknown session) / 400 (invalid body); genuine in-handler
  `return createErrorResponse(...)` paths (200 + success:false) left untouched.
- Reformat a few test files prettier flagged (pre-existing non-compliance).

Route suite: 307/307 passing (was 256/307). No production behavior change.

* test(respawn): mock child_process so AI checker never spawns real processes

respawn-controller.test.ts drives the AI idle checker (ai-checker-base), whose
runCheck() spawns a real `tmux new-session` running `claude -p`. The AI-enabled
tests only assert the ai_checking state transition (then cancel/stop), so the
spawn produced stray real tmux sessions and claude processes on every run — the
reason `npm test` (full suite) was unsafe to run inside a managed session.

Mock node:child_process here (mirroring ai-idle-checker.test.ts), spreading the
real module so `exec` stays intact for transitively-imported modules
(tmux-manager calls promisify(exec) at load). With this, the full non-mobile
suite runs without spawning any real tmux/claude.

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Co-authored-by: Teigen <teigen@TeigendeMac-mini.local>