feat(workbench): wire /health liveness probe into the status footer

The /health endpoint was the only W-026 API route with no UI consumer.
Surface it as a liveness indicator (colored dot + label) in the status
footer, isolated from /runtime/status so a live server still reads
"Healthy" even when runtime status is degraded.

- types: HealthStatus matching the server's {"status":"ok"} payload
- client: fetchHealth() with a short 3s timeout for fast failure
- queries: useHealth() polling every 15s, retry disabled
- footer: HealthIndicator rendered in both normal and degraded branches;
  any non-ok status fails safe to "Unhealthy"
- tests: healthy / errored / non-ok / checking / survives-runtime-failure

workbench-ui/src/api/client.ts

@@ -37,6 +37,7 @@ import type {
   MathProposalSummary,
   MathProposalDetail,
   MathRatifyResult,
+  HealthStatus,
 } from "../types/api";
 
 export class WorkbenchApiError extends Error {
@@ -71,6 +72,12 @@ export async function apiFetch<T>(
   }
 }
 
+export async function fetchHealth(): Promise<HealthStatus> {
+  // Cheap liveness probe — keep the timeout short so an unresponsive server
+  // surfaces as "Unhealthy" quickly rather than blocking the footer poll.
+  return apiFetch<HealthStatus>("/health", { timeoutMs: 3000 });
+}
+
 export async function fetchEvalLanes(): Promise<EvalLaneSummary[]> {
   const envelope = await apiFetch<{ lanes: EvalLaneSummary[] }>("/evals");
   return envelope.lanes;

workbench-ui/src/api/queries.ts

@@ -6,6 +6,7 @@ import {
 } from "@tanstack/react-query";
 import {
   apiFetch,
+  fetchHealth,
   fetchDemos,
   fetchEvalLanes,
   runEvalLane,
@@ -46,6 +47,7 @@ import {
 } from "./client";
 import type { WorkbenchApiError } from "./client";
 import type {
+  HealthStatus,
   RuntimeStatus,
   DemoRunResult,
   DemoSummary,
@@ -104,6 +106,17 @@ export function useRuntimeStatus() {
   });
 }
 
+export function useHealth() {
+  // Liveness probe — polled faster than runtime status and isolated from it so
+  // a healthy server still reads green even if /runtime/status is degraded.
+  return useQuery<HealthStatus, WorkbenchApiError>({
+    queryKey: ["api", "health"],
+    queryFn: fetchHealth,
+    refetchInterval: 15_000,
+    retry: false,
+  });
+}
+
 export function useArtifacts() {
   return useQuery<ArtifactRef[], WorkbenchApiError>({
     queryKey: ["api", "artifacts"],

workbench-ui/src/app/StatusFooter.test.tsx

@@ -3,14 +3,14 @@ import userEvent from "@testing-library/user-event";
 import { QueryClientProvider } from "@tanstack/react-query";
 import { afterEach, beforeEach, describe, expect, it, vi } from "vitest";
 import { createTestQueryClient } from "../test/createTestQueryClient";
-import type { RuntimeStatus } from "../types/api";
+import type { HealthStatus, RuntimeStatus } from "../types/api";
 
 vi.mock("../api/queries", async (importOriginal) => {
   const actual = await importOriginal<typeof import("../api/queries")>();
-  return { ...actual, useRuntimeStatus: vi.fn() };
+  return { ...actual, useRuntimeStatus: vi.fn(), useHealth: vi.fn() };
 });
 
-import { useRuntimeStatus } from "../api/queries";
+import { useHealth, useRuntimeStatus } from "../api/queries";
 import { StatusFooter } from "./StatusFooter";
 
 const status: RuntimeStatus = {
@@ -23,6 +23,17 @@ const status: RuntimeStatus = {
   mutation_mode: "read_only",
 };
 
+function mockHealth(
+  value: Partial<ReturnType<typeof useHealth>> & { data?: HealthStatus },
+) {
+  vi.mocked(useHealth).mockReturnValue({
+    data: undefined,
+    isError: false,
+    isLoading: false,
+    ...value,
+  } as unknown as ReturnType<typeof useHealth>);
+}
+
 function renderFooter() {
   return render(
     <QueryClientProvider client={createTestQueryClient()}>
@@ -36,6 +47,7 @@ beforeEach(() => {
     data: status,
     isError: false,
   } as unknown as ReturnType<typeof useRuntimeStatus>);
+  mockHealth({ data: { status: "ok" } });
 });
 
 afterEach(() => {
@@ -76,4 +88,50 @@ describe("StatusFooter", () => {
     expect(checkpoint.getAttribute("title")).toMatch(/checkpoint revision/i);
     expect(checkpoint.getAttribute("title")).toMatch(/unknown/);
   });
+
+  it("shows a healthy liveness indicator when GET /health reports ok", () => {
+    renderFooter();
+    const health = screen.getByTestId("health-indicator");
+    expect(health).toHaveAttribute("data-health", "healthy");
+    expect(health).toHaveTextContent("Healthy");
+  });
+
+  it("marks the server unhealthy when /health errors", () => {
+    mockHealth({ isError: true });
+    renderFooter();
+    const health = screen.getByTestId("health-indicator");
+    expect(health).toHaveAttribute("data-health", "unhealthy");
+    expect(health).toHaveTextContent("Unhealthy");
+  });
+
+  it("marks the server unhealthy when /health returns a non-ok status", () => {
+    mockHealth({ data: { status: "degraded" } });
+    renderFooter();
+    expect(screen.getByTestId("health-indicator")).toHaveAttribute(
+      "data-health",
+      "unhealthy",
+    );
+  });
+
+  it("shows a checking state before the first probe resolves", () => {
+    mockHealth({ isLoading: true });
+    renderFooter();
+    const health = screen.getByTestId("health-indicator");
+    expect(health).toHaveAttribute("data-health", "checking");
+    expect(health).toHaveTextContent("Checking");
+  });
+
+  it("still reports health when runtime status is unavailable", () => {
+    vi.mocked(useRuntimeStatus).mockReturnValue({
+      data: undefined,
+      isError: true,
+    } as unknown as ReturnType<typeof useRuntimeStatus>);
+    mockHealth({ data: { status: "ok" } });
+    renderFooter();
+    expect(screen.getByText("Status unavailable")).toBeInTheDocument();
+    expect(screen.getByTestId("health-indicator")).toHaveAttribute(
+      "data-health",
+      "healthy",
+    );
+  });
 });

workbench-ui/src/app/StatusFooter.tsx

@@ -1,8 +1,38 @@
 import { useState } from "react";
 import { useIsMutating } from "@tanstack/react-query";
-import { useRuntimeStatus } from "../api/queries";
+import { useHealth, useRuntimeStatus } from "../api/queries";
 import { useCopyToClipboard } from "../design/hooks/useCopyToClipboard";
 
+function HealthIndicator() {
+  const { data, isError, isLoading } = useHealth();
+  const healthy = !isError && data?.status === "ok";
+  const pending = isLoading && !data && !isError;
+
+  const label = pending ? "Checking" : healthy ? "Healthy" : "Unhealthy";
+  const dotColor = pending
+    ? "var(--color-state-neutral-text)"
+    : healthy
+      ? "var(--color-state-success-text)"
+      : "var(--color-state-danger-text)";
+
+  return (
+    <span
+      data-testid="health-indicator"
+      data-health={pending ? "checking" : healthy ? "healthy" : "unhealthy"}
+      className="flex items-center gap-1.5 text-[var(--color-text-secondary)]"
+      title="Server liveness probe (GET /health)"
+      aria-label={`Server health: ${label}`}
+    >
+      <span
+        aria-hidden="true"
+        className="inline-block h-2 w-2 rounded-full"
+        style={{ backgroundColor: dotColor }}
+      />
+      {label}
+    </span>
+  );
+}
+
 export function StatusFooter() {
   const { data, isError } = useRuntimeStatus();
   const chatTurnsPending = useIsMutating({ mutationKey: ["chat-turn"] }) > 0;
@@ -13,8 +43,9 @@ export function StatusFooter() {
     return (
       <footer
         data-region="statusfooter"
-        className="flex items-center border-t border-[var(--color-border-subtle)] bg-[var(--color-surface-base)] px-[var(--density-shell-padding-x)] py-[var(--density-footer-padding-y)] text-xs"
+        className="flex items-center gap-[var(--density-shell-gap)] border-t border-[var(--color-border-subtle)] bg-[var(--color-surface-base)] px-[var(--density-shell-padding-x)] py-[var(--density-footer-padding-y)] text-xs"
       >
+        <HealthIndicator />
         <span className="text-[var(--color-state-danger-text)]">Status unavailable</span>
       </footer>
     );
@@ -52,6 +83,8 @@ export function StatusFooter() {
       data-region="statusfooter"
       className="flex items-center gap-[var(--density-shell-gap)] border-t border-[var(--color-border-subtle)] bg-[var(--color-surface-base)] px-[var(--density-shell-padding-x)] py-[var(--density-footer-padding-y)] text-xs"
     >
+      <HealthIndicator />
+
       {mutationModeEl}
 
       <button

workbench-ui/src/types/api.ts

@@ -50,6 +50,10 @@ export type AuditSource =
   | "reboot_telemetry"
   | "teaching_proposal_log";
 
+export interface HealthStatus {
+  status: string;
+}
+
 export interface RuntimeStatus {
   backend: Backend;
   git_revision: string;