[arnav] remove 6 dead HTTP endpoints

Verified each had no production caller (frontend, electron, or
internal backend) — only test references kept them looking alive
to coverage tools. Drops ~140 LOC of route handlers + helpers.
- POST /api/outputs/vibe-code: never wired up; frontend has no
  vibe-code UI. Also drops VibeCodeRequest model and
  VIBE_CODE_SYSTEM_PROMPT.
- GET /api/service/cost-breakdown: frontend Usage page reads
  /usage-summary, which already returns by_model/by_provider.
- GET /api/service/status: zero callers; was placeholder.
- GET /api/service/spool/count: debug-only, no UI surface.
- GET /api/settings/default-system-prompt: frontend defines its
  own DEFAULT_SYSTEM_PROMPT in settingsSlice.ts and never fetches
  the backend constant.
- POST /api/browser/command: sole caller (browser_mcp_server.py
  subprocess) was deleted in 8286cc1; browser_agent.py now calls
  ws_manager.send_browser_command directly in-process.
Tests covering the removed endpoints are dropped along with the
now-unused mock-anthropic helpers in test_api_outputs.py.

backend/tests/test_api_settings.py

@@ -8,7 +8,7 @@ which we exercise here.
 Tests:
   - GET /api/settings returns defaults including the canned system prompt
   - PUT /api/settings round-trips a value and survives `load_settings()` reload
-  - default-system-prompt + reset-system-prompt
+  - reset-system-prompt
   - browse-directories on a tmp dir
 """
 
@@ -46,14 +46,6 @@ def test_put_round_trips_value(client):
     assert load_settings().theme == "light"
 
 
-def test_default_system_prompt_returns_constant(client):
-    from backend.apps.settings.models import DEFAULT_SYSTEM_PROMPT
-
-    resp = client.get("/api/settings/default-system-prompt")
-    assert resp.status_code == 200
-    assert resp.json()["default_system_prompt"] == DEFAULT_SYSTEM_PROMPT
-
-
 def test_reset_system_prompt(client):
     """Mutate then reset; the prompt must snap back to DEFAULT_SYSTEM_PROMPT."""
     from backend.apps.settings.models import DEFAULT_SYSTEM_PROMPT