feat: coord API — no-auth, DB softfail 503, agent tracking protocol

- coord routers: removed JWT auth requirement (internal-only endpoints)
- error_handler: SQLAlchemy OperationalError/DisconnectionError → 503
  with Retry-After: 30 header instead of 500
- /health: live DB probe (SELECT 1) instead of static response
- CLAUDE.md: "Live State Tracking" section with full agent protocol
  for all projects — session start, lock claim/release, component
  state updates, softfail + local queue catch-up
- COORDINATION_PROTOCOL.md: softfail/catch-up section + server-side
  503 behavior documented

Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>

api/middleware/error_handler.py

@@ -10,7 +10,7 @@ from typing import Any, Dict, Optional
 from fastapi import FastAPI, Request, status
 from fastapi.exceptions import RequestValidationError
 from fastapi.responses import JSONResponse
-from sqlalchemy.exc import SQLAlchemyError
+from sqlalchemy.exc import DisconnectionError, OperationalError, SQLAlchemyError
 
 
 class ClaudeToolsException(Exception):
@@ -278,6 +278,17 @@ async def sqlalchemy_exception_handler(
     )
 
 
+async def db_unavailable_exception_handler(request: Request, exc: Exception) -> JSONResponse:
+    return JSONResponse(
+        status_code=status.HTTP_503_SERVICE_UNAVAILABLE,
+        content={
+            "error": "Database unavailable. Retry after 30 seconds.",
+            "path": str(request.url.path),
+        },
+        headers={"Retry-After": "30"},
+    )
+
+
 async def generic_exception_handler(request: Request, exc: Exception) -> JSONResponse:
     """
     Handler for unhandled exceptions.
@@ -321,4 +332,6 @@ def register_exception_handlers(app: FastAPI) -> None:
     app.add_exception_handler(ClaudeToolsException, claudetools_exception_handler)
     app.add_exception_handler(RequestValidationError, validation_exception_handler)
     app.add_exception_handler(SQLAlchemyError, sqlalchemy_exception_handler)
+    app.add_exception_handler(OperationalError, db_unavailable_exception_handler)
+    app.add_exception_handler(DisconnectionError, db_unavailable_exception_handler)
     app.add_exception_handler(Exception, generic_exception_handler)