refactor(cleanup): remove legacy runtime directories and fix API semantics

Task 1: Clean up root-level runtime directories
- Backup live/, backtest/, production/ to runs/_legacy/
- Remove legacy directories from repo root

Task 2: API route semantics cleanup
- Create /api/runs/{run_id}/agents/* routes for runtime agent operations
- Keep /api/workspaces/{id}/agents/* for design-time (deprecated)
- Update frontend runtimeApi.js to use new /runs/ prefix
- Update legacy-inventory.md with completion status

New files:
- backend/api/runs.py - Runtime agent routes with proper run_id semantics

Modified:
- backend/api/__init__.py - Export runs_router
- backend/apps/agent_service.py - Include runs_router, update scope docs
- frontend/src/services/runtimeApi.js - Use /runs/ instead of /workspaces/
- docs/legacy-inventory.md - Mark cleanup as completed

Constraint: Maintain backward compatibility with old /workspaces/ routes
Rejected: Remove old routes entirely | need backward compatibility during transition
Confidence: high
Scope-risk: moderate
Directive: Old /api/workspaces/ routes remain functional but deprecated
Not-tested: Full integration test with active runtime

backend/apps/agent_service.py

@@ -11,7 +11,7 @@ from fastapi import FastAPI
 
 from backend.apps.cors import add_cors_middleware
 
-from backend.api import agents_router, guard_router, workspaces_router
+from backend.api import agents_router, guard_router, workspaces_router, runs_router
 from backend.agents import AgentFactory, WorkspaceManager, get_registry
 
 # Global instances (initialized on startup)
@@ -30,9 +30,9 @@ def _build_scope_payload(project_root: Path) -> dict[str, object]:
             "meaning": "Run-scoped runtime state and agent assets",
         },
         "agent_route_note": (
-            "On `/api/workspaces/{workspace_id}/agents/...`, design-time CRUD "
-            "routes still use `workspaces/`, while profile/skills/file routes "
-            "use `workspace_id` as a run id under `runs/<run_id>/`."
+            "Runtime routes use `/api/runs/{run_id}/agents/...`. "
+            "Legacy `/api/workspaces/{workspace_id}/agents/...` routes are deprecated "
+            "but remain for backward compatibility."
         ),
     }
 
@@ -96,6 +96,7 @@ def create_app(project_root: Path | None = None) -> FastAPI:
 
     app.include_router(workspaces_router)
     app.include_router(agents_router)
+    app.include_router(runs_router)
     app.include_router(guard_router)
     return app