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/e2e/fixtures.ts

@@ -222,11 +222,6 @@ export async function mockHermesApi(page: Page, options: MockHermesApiOptions =
       return
     }
 
-    if (pathname === '/api/hermes/pets/active') {
-      await route.fulfill(jsonResponse({ pet: null }))
-      return
-    }
-
     if (pathname === '/api/hermes/profiles') {
       await route.fulfill(jsonResponse({
         profiles: [