Fix: streak badge ignores user timezone

[Aryanshravan]

Fixes #3027

What

The streak SVG badge endpoint (/api/badge/streak-shield) always calculated
the current streak using UTC day boundaries, while the dashboard's streak
endpoint (/api/metrics/streak) correctly uses the user's stored timezone.
This caused the publicly embedded README badge to disagree with the
dashboard, particularly for users far from UTC around midnight.

Root cause

fetchStreak() in src/app/api/badge/streak-shield/route.ts called
calculateStreakFromDates(activeDates) without a timeZone argument, so it
silently defaulted to "UTC" — unlike other callers of the same function
(/api/metrics/streak, public-profile-data.ts, consistency-score.ts),
which all correctly resolve and pass the user's stored timezone.

Fix

• Added resolveUserTimeZone(), which looks up the user's stored
  timezone from Supabase by GitHub username (github_login).
• fetchStreak() now accepts a timeZone parameter (default "UTC") and
  passes it through to calculateStreakFromDates(activeDates, new Set(), timeZone).
• The GET handler resolves the timezone before calling fetchStreak.
• Falls back gracefully to "UTC" if the user has no DevTrack account, has
  no timezone set, or if the lookup fails for any reason — so the badge
  never breaks for unauthenticated/public lookups.

Testing

Added test/streak-shield-timezone.test.ts, covering:

• Badge correctly uses the user's stored timezone (not UTC) when set.
• Badge falls back to UTC when the user/timezone isn't found.
• Badge falls back to UTC gracefully if the timezone lookup throws (DB
  unavailable), and still returns a 200 response.

Acceptance criteria

• Badge streak count matches dashboard streak count for the same
  user/timezone.
• Unset/unknown timezone falls back to UTC without erroring.
• Existing badge rate-limiting and error-handling behavior unaffected.
• Test added covering timezone-aware badge streak calculation.

[github-actions]

GSSoC Label Checklist 🏷️

@Priyanshu-byte-coder — please apply the appropriate labels before merging:

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• level:beginner — 20 pts
• level:intermediate — 35 pts
• level:advanced — 55 pts
• level:critical — 80 pts

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• quality:exceptional — ×1.5 multiplier

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[Priyanshu-byte-coder]

CI is red (Build, Type check, Playwright) and the diff bundles unrelated leaderboard changes from #3010. Please rebase so this contains only the streak-badge timezone fix with green CI — the fix itself is in scope.

[Priyanshu-byte-coder]

Timezone-correct streak badges is worth fixing, but CI is red — Type check and Build fail on this branch. Fix those (pnpm type-check && pnpm build clean locally) and push; then I'll review the timezone logic against the badge endpoints.