feat: in-app notification center

[mschilling]

Summary

Users earn badges and level up, but there's no in-app notification center to celebrate these moments or surface them after they happen. Activity happens in the background (webhook → game engine → badge/level), but the user only discovers it when they happen to visit their profile.

Problem

• Badges are earned silently — no toast, no inbox, no celebration moment
• Level-ups happen without fanfare
• Users have no "unread" indicator for new achievements
• The bottom nav has no badge counts or notification dots

Proposed Solution

An in-app notification/inbox system that:

1. Stores notifications in Firestore (e.g., users/{userId}/notifications)
2. Triggers on key events: badge earned, level up, daily goal achieved, streak milestones
3. Shows unread count as a badge/dot on bottom navigation
4. Notification center UI: accessible from nav, shows recent notifications with read/unread state
5. Toast/celebration overlay: for high-impact events (badge earned, level up) when the user is active

Out of Scope (for now)

• Push notifications (FCM) — can be layered on later
• Email notifications
• Notification preferences/settings (beyond the existing toggle)

Related

• Bottom nav badge counts (feat: event handling improvements #14 from UX review)
• Settings: notification toggle already exists but does nothing yet