Add stats screen with backend endpoint and frontend page

Implements a dedicated /stats page showing cross-run aggregate statistics:
run overview with win rate, runs by game bar chart, encounter breakdowns,
top caught/encountered pokemon rankings, mortality analysis with death
causes, and type distribution. Backend endpoint uses aggregate SQL queries
to avoid N+1 fetching.

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

frontend/src/types/index.ts

@@ -1,3 +1,4 @@
 export * from './admin'
 export * from './game'
 export * from './rules'
+export * from './stats'

frontend/src/types/stats.ts

@@ -0,0 +1,51 @@
+export interface GameRunCount {
+  gameId: number
+  gameName: string
+  gameColor: string | null
+  count: number
+}
+
+export interface PokemonRanking {
+  pokemonId: number
+  name: string
+  spriteUrl: string | null
+  count: number
+}
+
+export interface DeathCause {
+  cause: string
+  count: number
+}
+
+export interface TypeCount {
+  type: string
+  count: number
+}
+
+export interface StatsResponse {
+  totalRuns: number
+  activeRuns: number
+  completedRuns: number
+  failedRuns: number
+  winRate: number | null
+  avgDurationDays: number | null
+
+  runsByGame: GameRunCount[]
+
+  totalEncounters: number
+  caughtCount: number
+  faintedCount: number
+  missedCount: number
+  catchRate: number | null
+  avgEncountersPerRun: number | null
+
+  topCaughtPokemon: PokemonRanking[]
+  topEncounteredPokemon: PokemonRanking[]
+
+  totalDeaths: number
+  mortalityRate: number | null
+  topDeathCauses: DeathCause[]
+  avgCatchLevel: number | null
+  avgFaintLevel: number | null
+  typeDistribution: TypeCount[]
+}