Explain gateway stopped states with Web UI diagnostics (#663)

* feat: add gateway diagnostics to Web UI status

* fix: improve gateway diagnostics mobile layout

tests/server/gateway-manager-diagnostics.test.ts

@@ -0,0 +1,57 @@
+import { afterEach, describe, expect, it, vi } from 'vitest'
+
+const readFileSyncMock = vi.fn()
+const existsSyncMock = vi.fn()
+
+vi.mock('fs', async importOriginal => {
+  const actual = await importOriginal<typeof import('fs')>()
+  return {
+    ...actual,
+    existsSync: existsSyncMock,
+    readFileSync: readFileSyncMock,
+  }
+})
+
+vi.mock('../../packages/server/src/services/hermes/hermes-path', () => ({
+  detectHermesHome: () => 'C:/Users/test/.hermes',
+  getHermesBin: () => 'hermes'
+}))
+
+describe('GatewayManager diagnostics', () => {
+  afterEach(() => {
+    vi.resetModules()
+    vi.clearAllMocks()
+  })
+
+  it('includes read-only diagnostics when a profile is stopped', async () => {
+    const yamlText = [
+      'platforms:',
+      '  api_server:',
+      '    extra:',
+      '      host: 127.0.0.1',
+      '      port: 8643',
+    ].join('\n')
+
+    existsSyncMock.mockImplementation((input: unknown) => {
+      const text = String(input)
+      return text.endsWith('config.yaml')
+    })
+    readFileSyncMock.mockImplementation((input: unknown) => {
+      const text = String(input)
+      if (text.endsWith('config.yaml')) {
+        return yamlText
+      }
+      return ''
+    })
+
+    const { GatewayManager } = await import('../../packages/server/src/services/hermes/gateway-manager')
+    const manager = new GatewayManager('default')
+    const status = await manager.detectStatus('default')
+
+    expect(status.running).toBe(false)
+    expect(status.diagnostics?.config_exists).toBe(true)
+    expect(status.diagnostics?.pid_file_exists).toBe(false)
+    expect(status.diagnostics?.reason).toBe('missing pid file')
+    expect(status.diagnostics?.health_url).toContain('/health')
+  })
+})