feat(gamification): align indicators engine with Sept 18 Vanishing Badges specification

[lucas-matw-unq]

Summary

Updates the adaptive gamification indicators engine to align with the revised Vanishing Badges specification (Sept 18, 2026), matching the updated simulator logic and removing obsolete indicator models.

Key Changes

• Indicators Replaced:
  • Replaced $ET_b$ (estimated time to award), $PMI$ / $relPMI$ (player motivation indicators), and $CMI$ (community motivation indicator) with the new definitions:
    • Def 3.1 Achievable Badges ($AB(p)$): Badges where player has earned all prerequisites and hasn't earned the badge yet.
    • Def 3.2 Individual Badge Interest ($i_3(p, b)$): Time elapsed since badge became achievable: $i_3(p, b) = 1 / (\text{asOfDate} - t_0(p, b))$.
    • Def 3.3 Player Ignored Badges ($\text{ignored_by}(p)$): Achievable badges with interest below the player's median interest across achievable badges.
    • Def 3.4 Community Ignored Indicator ($CII(b)$): Fraction of eligible players ignoring the badge: $|{p \in ep(b) : b \in \text{ignored_by}(p)}| / |ep(b)|$.
• Section 4.1 Trigger Evaluation:
  • Evaluates whether $\frac{\sum_{p \in P} |\text{ignored_by}(p)|}{\sum_{p \in P} |AB(p)|} \ge \text{threshold}$ (default 0.20, configurable via query parameter).
• Section 4.2.1 Candidate Selection:
  • Filters candidates to active badges that are not community-ignored ($CII(b) < 0.50$ when $ep(b) \ne \emptyset$).
  • Selects the candidate badge with the minimum $CII(b)$ score (adaptation candidate).
• DTOs & Controller:
  • Removed obsolete query parameters startDate and daysPerPeriod. Added optional threshold query param.
  • Updated CommunityIndicatorsResponseDto and BadgeIndicatorDto to expose full mathematical trace (isTriggered, triggerBadges, candidateBadges, lowestCII, adaptationCandidateBadge, achievableBadges, ignoredBadges, individualInterest).
• Documentation:
  • Updated docs/adaptive-gamification/indicators-engine.md with the new definitions, formulas, workflows, and response payloads.
• Tests:
  • Updated unit tests across strategy, service, and controller; all 57 suites (466 tests) pass.

Refs: #22