[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_agents.py

@@ -8,7 +8,6 @@ Tests:
     succeeds; DELETE removes it.
   - POST /sessions/{id}/edit_message validates input.
   - PATCH /sessions/{id} updates allowed fields (name, system_prompt).
-  - GET /sessions/{id}/branches returns the default 'main' branch.
   - GET /history returns paginated results.
 """
 
@@ -127,20 +126,6 @@ def test_patch_session_updates_name(client, stub_agent_loop):
     assert fetched["model"] == "sonnet"  # not changed by the PATCH
 
 
-def test_get_branches_returns_main(client, stub_agent_loop):
-    launch = client.post(
-        "/api/agents/launch",
-        json={"name": "B", "model": "sonnet", "mode": "agent"},
-    )
-    session_id = launch.json()["session_id"]
-
-    resp = client.get(f"/api/agents/sessions/{session_id}/branches")
-    assert resp.status_code == 200
-    body = resp.json()
-    assert body["active_branch_id"] == "main"
-    assert "main" in body["branches"]
-
-
 def test_history_endpoint_returns_paginated_shape(client):
     """`/history` is the search-and-resume endpoint. Even with no
     saved sessions it should return the paginated wrapper without