[Scepter00]

Closes #450
Summary

• Add hierarchical categories with parent links, ordering, slug support, and cycle prevention.
• Add category analytics for puzzle counts, attempts, and completions.
• Extend puzzle search to match categories and relational tags.
• Add trending tags based on recently published puzzles.
• Prevent duplicate tags from inflating puzzle associations and usage counts.
• Improve recommendations by ranking puzzles using completions and ratings.
• Add category hierarchy and analytics tests, plus a production migration.
  Verification
• git diff --check passed.
• Typecheck and Jest tests could not run because dependencies are not installed (tsc not found).

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