Add egglocke, wonderlocke, and randomizer variant rules

When any variant rule is enabled, the encounter modal switches from
the game's regional dex to an all-Pokemon search (same debounced
API pattern as EggEncounterModal). A new "Run Variant" section in
rules configuration groups these rules, and badges render in amber.

Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>

frontend/src/types/rules.ts

@@ -8,6 +8,11 @@ export interface NuzlockeRules {
   // Playstyle (informational, for stats/categorization)
   hardcoreMode: boolean
   setModeOnly: boolean
+
+  // Variant (changes which Pokemon can appear)
+  egglocke: boolean
+  wonderlocke: boolean
+  randomizer: boolean
 }
 
 export const DEFAULT_RULES: NuzlockeRules = {
@@ -20,13 +25,18 @@ export const DEFAULT_RULES: NuzlockeRules = {
   // Playstyle - off by default
   hardcoreMode: false,
   setModeOnly: false,
+
+  // Variant - off by default
+  egglocke: false,
+  wonderlocke: false,
+  randomizer: false,
 }
 
 export interface RuleDefinition {
   key: keyof NuzlockeRules
   name: string
   description: string
-  category: 'core' | 'playstyle'
+  category: 'core' | 'playstyle' | 'variant'
 }
 
 export const RULE_DEFINITIONS: RuleDefinition[] = [
@@ -74,4 +84,27 @@ export const RULE_DEFINITIONS: RuleDefinition[] = [
       'The game must be played in "Set" battle style, meaning you cannot switch Pokémon after knocking out an opponent.',
     category: 'playstyle',
   },
+
+  // Variant
+  {
+    key: 'egglocke',
+    name: 'Egglocke',
+    description:
+      'All caught Pokémon are replaced with traded eggs. The encounter selector shows all Pokémon since the hatched species is unknown.',
+    category: 'variant',
+  },
+  {
+    key: 'wonderlocke',
+    name: 'Wonderlocke',
+    description:
+      'All caught Pokémon are Wonder Traded away. The encounter selector shows all Pokémon since the received species is unknown.',
+    category: 'variant',
+  },
+  {
+    key: 'randomizer',
+    name: 'Randomizer',
+    description:
+      "The ROM's wild Pokémon are randomized, so the encounter selector shows all Pokémon instead of the game's regional dex.",
+    category: 'variant',
+  },
 ]