refactor(notifications): unify notification UX into sidebar and add rich feed interactions

[justjxke]

Why

• Replace the old /notifications page flow with a single right-sidebar notifications experience.
• Improve clarity and actionability of notifications (status context, per-item actions, filtering, bulk actions).
• Iterate quickly on UI with dummy seeded notifications for local validation.

How

• Removed page-based notifications surface and consolidated behavior in the sidebar feed.
• Added richer notification model + UI:
  • status chips, contextual secondary text, grouped sections, tab filters
  • select mode, bulk actions, mute/unmute flow, undo for mark-as-read
  • improved hover/selection/action affordances and header controls
• Added extensive dummy notification data for realistic local stress-testing and visual QA.
• Added safeguards for non-numeric demo IDs in mark-read flow to avoid GitHub API 404s.

Tests

• pnpm fmt:check
• pnpm typecheck
• pnpm lint (existing repo warnings unchanged, no new errors)

Draft note

This PR is intentionally Draft because it still contains demo/dummy notification data used for local development and UX validation.
Before merge, we should remove or fully gate dummy notification paths for production.

Notes

I'd heavily appreciate design feedback, what you want removed, added, changed ect. This took quite a while, most of it brainstorming on the design and interaction flow. There's definitely room for improvement.

Screenshots

[vercel]

@justjxke is attempting to deploy a commit to the better-auth Team on Vercel.

A member of the Team first needs to authorize it.

[justjxke]

hmmm i should work on this again and improve the UI but idk if it's worth it.