Finish interrupted features: tab prefetch, pet viewport, and home logo.

Add shared quiz/habits tab cache with nav hover prefetch and AppDataPrefetcher,
make the pet screen fill and center the viewport, and point the HaBit logo to /.

components/avatar/avatar-page-content.tsx

@@ -45,5 +45,5 @@ export function AvatarPageContent() {
     );
   }
 
-  return <PetHabitat customization={customization} />;
+  return <PetHabitat customization={customization} fillViewport />;
 }