feat: add health check endpoint for agent authentication status

backend/app/schemas/health.py

@@ -2,6 +2,8 @@
 
 from __future__ import annotations
 
+from uuid import UUID
+
 from pydantic import Field
 from sqlmodel import SQLModel
 
@@ -13,3 +15,29 @@ class HealthStatusResponse(SQLModel):
         description="Indicates whether the probe check succeeded.",
         examples=[True],
     )
+
+
+class AgentHealthStatusResponse(HealthStatusResponse):
+    """Agent-authenticated liveness payload for agent route probes."""
+
+    agent_id: UUID = Field(
+        description="Authenticated agent id derived from `X-Agent-Token`.",
+        examples=["aaaaaaaa-aaaa-aaaa-aaaa-aaaaaaaaaaaa"],
+    )
+    board_id: UUID | None = Field(
+        default=None,
+        description="Board scope for the authenticated agent, when applicable.",
+        examples=["bbbbbbbb-bbbb-bbbb-bbbb-bbbbbbbbbbbb"],
+    )
+    gateway_id: UUID = Field(
+        description="Gateway owning the authenticated agent.",
+        examples=["cccccccc-cccc-cccc-cccc-cccccccccccc"],
+    )
+    status: str = Field(
+        description="Current persisted lifecycle status for the authenticated agent.",
+        examples=["online", "healthy", "updating"],
+    )
+    is_board_lead: bool = Field(
+        description="Whether the authenticated agent is the board lead.",
+        examples=[False],
+    )