[DISC-003] Add match ranking and compatibility score

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Outline

Summary

Ranks the discovery feed by language compatibility for signed-in viewers and surfaces a concise reason on each profile card explaining why it is a good match.

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Changes & Enhancements

• Type of Change:
  • Feature
  • Bugfix
  • Refactor
  • Chore
• Changes:
  • (discovery):
    • Add a deterministic, tunable compatibility scorer over native/target languages, proficiency, timezone proximity, and shared interests.
    • Add a Best match sort that ranks results for signed-in viewers and becomes their default; logged-out discovery keeps general sorting.
    • Show a concise match reason on each profile card (for example, learning each other's native languages).
  • (discovery feed):
    • Thread the signed-in viewer's stored profile from the server page into the feed.
  • (cleanup):
    • Remove the inert useProfileMatching hook, superseded by the scoring module.
  • (i18n):
    • Add Best match and match-reason strings for en and ja.
  • (storybook):
    • Add stories and play assertions for the match reason variants and best-match ranking.

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Page / App Changes

Affected Next.js Routes (Local):

• /[lang] (discovery feed)

Before (Screenshot)

After (Screenshot)

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Component / Storybook Changes

Affected Storybook Components (Local):

• Discovery/ProfileCard > MatchReasonMutual
• Discovery/DiscoveryPage > BestMatch

Before (Screenshot)

After (Screenshot)

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Not Doing

• Goal-based weighting is omitted: per-target learning goals are not persisted (only language and level), so there is no goal data to rank on.

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Other (Remarks)

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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.