feat(api): add luck (LUK) stat to character system

Add new Luck stat to the character stats system with class-specific values:
- Assassin: 12 (highest - critical specialists)
- Luminary: 11 (divine favor)
- Wildstrider/Lorekeeper: 10 (average)
- Arcanist/Oathkeeper: 9 (modest)
- Vanguard: 8 (default - relies on strength)
- Necromancer: 7 (lowest - dark arts cost)

Changes:
- Add luck field to Stats dataclass with default of 8
- Add LUCK to StatType enum
- Update all 8 class YAML files with luck values
- Display LUK in character panel (play page) and detail page
- Update DATA_MODELS.md documentation

Backward compatible: existing characters without luck default to 8.

api/docs/DATA_MODELS.md

@@ -50,6 +50,7 @@ All enum types are defined in `/app/models/enums.py` for type safety throughout
 | `INTELLIGENCE` | Magical power |
 | `WISDOM` | Perception and insight |
 | `CHARISMA` | Social influence |
+| `LUCK` | Fortune and fate (affects crits, loot, random outcomes) |
 
 ### AbilityType
 
@@ -597,14 +598,15 @@ success = service.soft_delete_message(
 
 ### Stats
 
-| Field | Type | Description |
-|-------|------|-------------|
-| `strength` | int | Physical power |
-| `dexterity` | int | Agility and precision |
-| `constitution` | int | Endurance and health |
-| `intelligence` | int | Magical power |
-| `wisdom` | int | Perception and insight |
-| `charisma` | int | Social influence |
+| Field | Type | Default | Description |
+|-------|------|---------|-------------|
+| `strength` | int | 10 | Physical power |
+| `dexterity` | int | 10 | Agility and precision |
+| `constitution` | int | 10 | Endurance and health |
+| `intelligence` | int | 10 | Magical power |
+| `wisdom` | int | 10 | Perception and insight |
+| `charisma` | int | 10 | Social influence |
+| `luck` | int | 8 | Fortune and fate (affects crits, loot, random outcomes) |
 
 **Derived Properties (Computed):**
 - `hit_points` = 10 + (constitution × 2)
@@ -614,6 +616,8 @@ success = service.soft_delete_message(
 
 **Note:** Defense and resistance are computed properties, not stored values. They are calculated on-the-fly from constitution and wisdom.
 
+**Luck Stat:** The luck stat has a lower default (8) compared to other stats (10). Each class has a specific luck value ranging from 7 (Necromancer) to 12 (Assassin). Luck will influence critical hit chance, hit/miss calculations, base damage variance, NPC interactions, loot generation, and spell power in future implementations.
+
 ### SkillNode
 
 | Field | Type | Description |
@@ -662,16 +666,26 @@ success = service.soft_delete_message(
 
 ### Initial 8 Player Classes
 
-| Class | Theme | Skill Tree 1 | Skill Tree 2 |
-|-------|-------|--------------|--------------|
-| **Vanguard** | Tank/melee | Defensive (shields, armor, taunts) | Offensive (weapon mastery, heavy strikes) |
-| **Assassin** | Stealth/critical | Assassination (critical hits, poisons) | Shadow (stealth, evasion) |
-| **Arcanist** | Elemental spells | Pyromancy (fire spells, DoT) | Cryomancy (ice spells, crowd control) |
-| **Luminary** | Healing/support | Holy (healing, buffs) | Divine Wrath (smite, undead damage) |
-| **Wildstrider** | Ranged/nature | Marksmanship (bow skills, critical shots) | Beast Master (pet companion, nature magic) |
-| **Oathkeeper** | Hybrid tank/healer | Protection (defensive auras, healing) | Retribution (holy damage, smites) |
-| **Necromancer** | Death magic/summon | Dark Arts (curses, life drain) | Summoning (undead minions) |
-| **Lorekeeper** | Support/control | Performance (buffs, debuffs via music) | Trickery (illusions, charm) |
+| Class | Theme | LUK | Skill Tree 1 | Skill Tree 2 |
+|-------|-------|-----|--------------|--------------|
+| **Vanguard** | Tank/melee | 8 | Defensive (shields, armor, taunts) | Offensive (weapon mastery, heavy strikes) |
+| **Assassin** | Stealth/critical | 12 | Assassination (critical hits, poisons) | Shadow (stealth, evasion) |
+| **Arcanist** | Elemental spells | 9 | Pyromancy (fire spells, DoT) | Cryomancy (ice spells, crowd control) |
+| **Luminary** | Healing/support | 11 | Holy (healing, buffs) | Divine Wrath (smite, undead damage) |
+| **Wildstrider** | Ranged/nature | 10 | Marksmanship (bow skills, critical shots) | Beast Master (pet companion, nature magic) |
+| **Oathkeeper** | Hybrid tank/healer | 9 | Protection (defensive auras, healing) | Retribution (holy damage, smites) |
+| **Necromancer** | Death magic/summon | 7 | Dark Arts (curses, life drain) | Summoning (undead minions) |
+| **Lorekeeper** | Support/control | 10 | Performance (buffs, debuffs via music) | Trickery (illusions, charm) |
+
+**Class Luck Values:**
+- **Assassin (12):** Highest luck - critical strike specialists benefit most from fortune
+- **Luminary (11):** Divine favor grants above-average luck
+- **Wildstrider (10):** Average luck - self-reliant nature
+- **Lorekeeper (10):** Average luck - knowledge is their advantage
+- **Arcanist (9):** Slight chaos magic influence
+- **Oathkeeper (9):** Honorable path grants modest fortune
+- **Vanguard (8):** Relies on strength and skill, not luck
+- **Necromancer (7):** Lowest luck - dark arts exact a toll
 
 **Extensibility:** Class system designed to easily add more classes in future updates.