feat(routes-f): moon phase calculator

[dmystical-coder]

Summary

Implements the moon phase calculator (#791).

GET /api/routes-f/moon-phase?date=YYYY-MM-DD → { phase_name, illumination_percent, age_days }

Approach

• Documented synodic-month approximation: reference new moon epoch 2000-01-06 18:14 UTC and mean synodic month 29.53058867 days (Meeus, Astronomical Algorithms). Lunar age is the elapsed time since the epoch reduced modulo the synodic month.
• Illumination = (1 − cos(2π·age/synodic)) / 2.
• Eight phases (new, waxing crescent, first quarter, waxing gibbous, full, waning gibbous, last quarter, waning crescent) selected by nearest-eighth rounding so the principal phases sit on their exact ages.
• Rejects malformed and impossible calendar dates (2024-02-30) via a component round-trip, since new Date(...) silently rolls overflow days into the next month.

Tests

Validated against NASA new moons (2024-01-11, 2025-01-29) and full moons (2024-01-25, 2025-01-13), plus epoch, half-cycle, a full eight-phase walk, range invariants, and the route's 400 paths.

Scope

All files live under app/api/routes-f/moon-phase/; the only import is the existing in-folder _lib/validate helper, matching the merged fiscal-quarter/deep-merge routes.

Closes #791

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