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 /.

lib/app-tab-data-cache.ts

@@ -0,0 +1,122 @@
+import type { AvatarCondition, DailyQuizSubmission } from "@/lib/avatar-state";
+import type { DailyTask } from "@/lib/daily-tasks";
+import { getDailyTasks } from "@/lib/daily-tasks";
+import {
+  getAvatarConditionForToday,
+  getDailyEntryForToday,
+  hasCompletedDailyQuizToday,
+} from "@/lib/daily-quiz-storage";
+import { getCustomHabits, type Habit } from "@/lib/habits-storage";
+import { getProfilePreferences } from "@/lib/profile-preferences-storage";
+
+export type QuizTabData = {
+  submission: DailyQuizSubmission | null;
+  liveCondition: AvatarCondition | null;
+};
+
+export type HabitsTabData = {
+  dailyTasks: DailyTask[];
+  customHabits: Habit[];
+  focusTopic: string | null;
+  quizCompletedToday: boolean;
+};
+
+let quizCache: QuizTabData | null = null;
+let habitsCache: HabitsTabData | null = null;
+let quizInflight: Promise<QuizTabData> | null = null;
+let habitsInflight: Promise<HabitsTabData> | null = null;
+
+export function getCachedQuizTabData() {
+  return quizCache;
+}
+
+export function getCachedHabitsTabData() {
+  return habitsCache;
+}
+
+export function invalidateAppTabDataCache() {
+  quizCache = null;
+  habitsCache = null;
+}
+
+async function loadQuizTabData(): Promise<QuizTabData> {
+  const submission = await getDailyEntryForToday();
+
+  if (submission) {
+    return {
+      submission,
+      liveCondition: submission.condition,
+    };
+  }
+
+  return {
+    submission: null,
+    liveCondition: await getAvatarConditionForToday(),
+  };
+}
+
+async function loadHabitsTabData(): Promise<HabitsTabData> {
+  const [dailyTasks, customHabits, preferences, quizCompletedToday] =
+    await Promise.all([
+      getDailyTasks(),
+      getCustomHabits(),
+      getProfilePreferences(),
+      hasCompletedDailyQuizToday(),
+    ]);
+
+  return {
+    dailyTasks,
+    customHabits,
+    focusTopic: preferences.focusTopic,
+    quizCompletedToday,
+  };
+}
+
+export async function prefetchQuizTabData(options?: { force?: boolean }) {
+  if (!options?.force && quizCache) {
+    return quizCache;
+  }
+
+  if (quizInflight) {
+    return quizInflight;
+  }
+
+  quizInflight = loadQuizTabData()
+    .then((data) => {
+      quizCache = data;
+      return data;
+    })
+    .finally(() => {
+      quizInflight = null;
+    });
+
+  return quizInflight;
+}
+
+export async function prefetchHabitsTabData(options?: { force?: boolean }) {
+  if (!options?.force && habitsCache) {
+    return habitsCache;
+  }
+
+  if (habitsInflight) {
+    return habitsInflight;
+  }
+
+  habitsInflight = loadHabitsTabData()
+    .then((data) => {
+      habitsCache = data;
+      return data;
+    })
+    .finally(() => {
+      habitsInflight = null;
+    });
+
+  return habitsInflight;
+}
+
+export async function prefetchAppTabData(options?: { force?: boolean }) {
+  await Promise.all([
+    prefetchQuizTabData(options),
+    prefetchHabitsTabData(options),
+  ]);
+}