[DISC-007] Add availability and timezone overlap

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Outline

Summary

DISC-007 makes profile availability a first-class discovery signal: it persists each member's weekly availability window, computes timezone-aware overlap against the signed-in viewer, and surfaces it across the feed and profile editor.

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Changes & Enhancements

• Type of Change:
  • Feature
  • Bugfix
  • Refactor
  • Chore
• Changes:
  • (overlap engine):
    • Add a pure module that maps availability windows into UTC week intervals and reports overlap minutes, meaningful overlap, and available-now state.
    • Share DST-aware timezone offset and time parsing helpers from the availability constants.
  • (data model):
    • Persist structured availability (days, from, to, any-time) and a hide-availability flag alongside the legacy coarse preset, with a back-compatible migration.
    • Read the structured window in discovery and the profile editor, falling back to the preset for older rows.
  • (discovery):
    • Add "Available now" and "Overlaps with me" filters plus a "Most overlap" sort, persisted in the URL.
    • Thread the viewer's timezone and availability into the feed and show an overlap or available-now badge with viewer-local times on each card.
  • (profile):
    • Add a privacy toggle to hide exact availability from the public profile.

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Page / App Changes

Affected Next.js Routes (Local):

• /[lang]
• /[lang]/profile

Before (Screenshot)

After (Screenshot)

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Component / Storybook Changes

Affected Storybook Components (Local):

• Discovery/ProfileCard > AvailabilityOverlap
• Discovery/ProfileCard > AvailableNow
• Discovery/DiscoveryPage > AvailabilityFilter

Before (Screenshot)

After (Screenshot)

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Not Doing

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Other (Remarks)

Includes an additive, back-compatible migration (0004_availability_overlap.sql); deploy needs bun run db:migrate.

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Checklists

• Code is well-documented (comments, JSDoc, etc.).
• Existing comments were updated as needed.
• No out-of-scope changes are included.
• Write TODO comments where future work is required.
• Removed unnecessary debug code (e.g., console.log, debugger).
• Self-reviewed and tested locally.