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.

packages/client/src/components/layout/AppSidebar.vue

@@ -153,15 +153,6 @@ function handleUpdateClick() {
             </svg>
             <span>{{ t("sidebar.mcp") }}</span>
           </RouteLinkItem>
-          <RouteLinkItem class="nav-item" :to="{ name: 'hermes.petdex' }" :active="selectedKey === 'hermes.petdex'">
-            <svg width="16" height="16" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="1.5" stroke-linecap="round" stroke-linejoin="round">
-              <path d="M12 3l7 4v6c0 4-3 7-7 8-4-1-7-4-7-8V7l7-4z" />
-              <path d="M9 11h.01" />
-              <path d="M15 11h.01" />
-              <path d="M9.5 15c1.6 1.1 3.4 1.1 5 0" />
-            </svg>
-            <span>{{ t("sidebar.petdex") }}</span>
-          </RouteLinkItem>
           <RouteLinkItem class="nav-item" :to="{ name: 'hermes.memory' }" :active="selectedKey === 'hermes.memory'">
             <svg width="16" height="16" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="1.5" stroke-linecap="round" stroke-linejoin="round">
               <path d="M9 18h6" />