remove the desktop-pet system

The pet feature was three loosely coupled subsystems that no core flow
depended on: the Petdex catalog page, the pet install/preference store, and
the pet-state socket. All three are removed.

The only cross-boundary touch point was a try/catch-wrapped observer that
mapped chat-run events to pet animations. Removing it leaves the /chat-run
event contract unchanged: no event name, field name, field type, or emission
timing changed.

Removing petdexPublicRoutes also closes the unauthenticated outbound proxy
at /api/hermes/petdex/asset, which shrinks the SSRF surface.

tests/client/pets-store.test.ts

@@ -1,58 +0,0 @@
-// @vitest-environment jsdom
-import { beforeEach, describe, expect, it, vi } from 'vitest'
-import { createPinia, setActivePinia } from 'pinia'
-import type { ActivePet } from '@/api/hermes/pets'
-
-const mockPetsApi = vi.hoisted(() => ({
-  fetchActivePet: vi.fn(),
-  adoptPet: vi.fn(),
-  updateActivePetPreferences: vi.fn(),
-}))
-
-vi.mock('@/api/hermes/pets', () => mockPetsApi)
-
-import { usePetsStore } from '@/stores/hermes/pets'
-
-function activePet(overrides: Partial<ActivePet> = {}): ActivePet {
-  return {
-    enabled: true,
-    slug: 'desk-cat',
-    displayName: 'Desk Cat',
-    kind: 'cat',
-    submittedBy: 'petdex',
-    source: 'petdex',
-    mime: 'image/webp',
-    spritesheetDataUrl: 'data:image/webp;base64,AA==',
-    spritesheetRevision: 1,
-    frameW: 192,
-    frameH: 208,
-    framesPerState: 6,
-    loopMs: 1100,
-    scale: 0.33,
-    position: { x: 10, y: 20 },
-    stateRows: ['idle'],
-    installedAt: 1,
-    updatedAt: 1,
-    ...overrides,
-  }
-}
-
-describe('Pets Store', () => {
-  beforeEach(() => {
-    setActivePinia(createPinia())
-    vi.clearAllMocks()
-  })
-
-  it('disables and clears the active pet when hiding it', async () => {
-    const store = usePetsStore()
-    store.activePet = activePet()
-    mockPetsApi.updateActivePetPreferences.mockResolvedValue(null)
-
-    await store.hideActivePet()
-
-    expect(mockPetsApi.updateActivePetPreferences).toHaveBeenCalledWith({ enabled: false })
-    expect(store.activePet).toBeNull()
-    expect(store.hasActivePet).toBe(false)
-    expect(store.saving).toBe(false)
-  })
-})