Add egg encounter logging with route-lock bypass

Egg hatches can now be logged at any location without consuming the
route's encounter slot. Adds an EggEncounterModal with pokemon search
and a "Log Egg" button on the run encounters page.

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

frontend/src/pages/RunEncounters.tsx

@@ -6,6 +6,7 @@ import { useCreateEncounter, useUpdateEncounter, useBulkRandomize } from '../hoo
 import { usePokemonFamilies } from '../hooks/usePokemon'
 import { useGameBosses, useBossResults, useCreateBossResult } from '../hooks/useBosses'
 import {
+  EggEncounterModal,
   EncounterModal,
   EncounterMethodBadge,
   StatCard,
@@ -410,6 +411,7 @@ export function RunEncounters() {
     useState<EncounterDetail | null>(null)
   const [showEndRun, setShowEndRun] = useState(false)
   const [showShinyModal, setShowShinyModal] = useState(false)
+  const [showEggModal, setShowEggModal] = useState(false)
   const [expandedBosses, setExpandedBosses] = useState<Set<number>>(new Set())
   const [showTeam, setShowTeam] = useState(true)
   const [filter, setFilter] = useState<'all' | RouteStatus>('all')
@@ -675,6 +677,7 @@ export function RunEncounters() {
         setSelectedRoute(null)
         setEditingEncounter(null)
         setShowShinyModal(false)
+        setShowEggModal(false)
       },
     })
   }
@@ -752,6 +755,14 @@ export function RunEncounters() {
                 &#10022; Log Shiny
               </button>
             )}
+            {isActive && (
+              <button
+                onClick={() => setShowEggModal(true)}
+                className="px-3 py-1 text-sm border border-green-400 dark:border-green-600 text-green-600 dark:text-green-400 rounded-full font-medium hover:bg-green-50 dark:hover:bg-green-900/20 transition-colors"
+              >
+                &#x1F95A; Log Egg
+              </button>
+            )}
             {isActive && (
               <button
                 onClick={() => setShowEndRun(true)}
@@ -1257,6 +1268,16 @@ export function RunEncounters() {
         />
       )}
 
+      {/* Egg Encounter Modal */}
+      {showEggModal && routes && (
+        <EggEncounterModal
+          routes={routes}
+          onSubmit={handleCreate}
+          onClose={() => setShowEggModal(false)}
+          isPending={createEncounter.isPending}
+        />
+      )}
+
       {/* Status Change Modal (team pokemon) */}
       {selectedTeamEncounter && (
         <StatusChangeModal