feat(cli): live "say hi" probe for server LLMs in mcpctl status

Status was showing the server-side LLM list but not whether each one
actually serves inference. This adds a per-LLM probe that POSTs a
tiny prompt to /api/v1/llms/<name>/infer:

  messages: [{ role: 'user', content: "Say exactly the word 'hi' and nothing else." }]
  max_tokens: 8, temperature: 0

Each registered LLM gets a one-line health line:

  Server LLMs: 2 registered (probing live "say hi"...)
    fast   qwen3-thinking  ✓ "hi" 312ms
              openai → qwen3-thinking  http://litellm.../v1  key:litellm/API_KEY
    heavy  sonnet  ✗ upstream auth failed: 401
              anthropic → claude-sonnet-4-5  provider default  no key

Probes run in parallel so a single slow LLM doesn't gate the others;
each has its own 15-second timeout. JSON/YAML output gains a
\`health: { ok, ms, say?, error? }\` field per server LLM so dashboards
get the same liveness signal.

Tests: 25/25 (was 24, +1 new for the failure-path render). Workspace
suite: 2006/2006 across 149 files.

Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>

src/cli/tests/commands/status.test.ts

@@ -28,6 +28,7 @@ function baseDeps(overrides?: Partial<StatusCommandDeps>): Partial<StatusCommand
     checkHealth: async () => true,
     fetchProviders: async () => null,
     fetchServerLlms: async () => null,
+    probeServerLlm: async () => ({ ok: true, ms: 12, say: 'hi' }),
     isTTY: false,
     ...overrides,
   };
@@ -210,14 +211,33 @@ describe('status command', () => {
         { id: 'l1', name: 'qwen3-thinking', type: 'openai', model: 'qwen3-thinking', tier: 'fast', url: 'http://x:4000/v1', apiKeyRef: { name: 'litellm', key: 'API_KEY' } },
         { id: 'l2', name: 'sonnet', type: 'anthropic', model: 'claude-sonnet-4-5', tier: 'heavy', url: '', apiKeyRef: null },
       ],
+      probeServerLlm: async () => ({ ok: true, ms: 42, say: 'hi' }),
     }));
     await cmd.parseAsync([], { from: 'user' });
     const out = output.join('\n');
     expect(out).toContain('Server LLMs: 2 registered');
-    expect(out).toContain('qwen3-thinking (openai → qwen3-thinking)');
-    expect(out).toContain('sonnet (anthropic → claude-sonnet-4-5)');
+    expect(out).toContain('qwen3-thinking');
+    expect(out).toContain('openai → qwen3-thinking');
+    expect(out).toContain('sonnet');
+    expect(out).toContain('anthropic → claude-sonnet-4-5');
     expect(out).toMatch(/fast\s+qwen3-thinking/);
     expect(out).toMatch(/heavy\s+sonnet/);
+    // Health probe result rendered for each LLM
+    expect(out).toContain('✓ "hi" 42ms');
+  });
+
+  it('renders a failed "say hi" probe with the error message', async () => {
+    const cmd = createStatusCommand(baseDeps({
+      fetchServerLlms: async () => [
+        { id: 'l1', name: 'broken', type: 'openai', model: 'gpt-4o', tier: 'fast', url: 'http://x', apiKeyRef: null },
+      ],
+      probeServerLlm: async () => ({ ok: false, ms: 5000, error: 'upstream auth failed: 401' }),
+    }));
+    await cmd.parseAsync([], { from: 'user' });
+    const out = output.join('\n');
+    expect(out).toContain('Server LLMs: 1 registered');
+    expect(out).toContain('broken');
+    expect(out).toContain('✗ upstream auth failed: 401');
   });
 
   it('renders "none registered" when mcpd has no Llm rows', async () => {
@@ -254,13 +274,22 @@ describe('status command', () => {
     expect(capturedToken).toBeNull();
   });
 
-  it('includes serverLlms in JSON output', async () => {
+  it('includes serverLlms with probed health in JSON output', async () => {
     const llms = [
       { id: 'l1', name: 'qwen3-thinking', type: 'openai', model: 'qwen3-thinking', tier: 'fast', url: 'http://x', apiKeyRef: null },
     ];
-    const cmd = createStatusCommand(baseDeps({ fetchServerLlms: async () => llms }));
+    const cmd = createStatusCommand(baseDeps({
+      fetchServerLlms: async () => llms,
+      probeServerLlm: async () => ({ ok: true, ms: 99, say: 'hi' }),
+    }));
     await cmd.parseAsync(['-o', 'json'], { from: 'user' });
-    const parsed = JSON.parse(output[0]) as { serverLlms?: typeof llms };
-    expect(parsed.serverLlms).toEqual(llms);
+    const parsed = JSON.parse(output[0]) as {
+      serverLlms?: Array<typeof llms[number] & { health: { ok: boolean; ms: number; say?: string } }>;
+    };
+    expect(parsed.serverLlms).toHaveLength(1);
+    expect(parsed.serverLlms![0]).toMatchObject({
+      name: 'qwen3-thinking',
+      health: { ok: true, ms: 99, say: 'hi' },
+    });
   });
 });