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>

backend/src/app/schemas/stats.py

@@ -0,0 +1,58 @@
+from app.schemas.base import CamelModel
+
+
+class GameRunCount(CamelModel):
+    game_id: int
+    game_name: str
+    game_color: str | None
+    count: int
+
+
+class PokemonRanking(CamelModel):
+    pokemon_id: int
+    name: str
+    sprite_url: str | None
+    count: int
+
+
+class DeathCause(CamelModel):
+    cause: str
+    count: int
+
+
+class TypeCount(CamelModel):
+    type: str
+    count: int
+
+
+class StatsResponse(CamelModel):
+    # Run overview
+    total_runs: int
+    active_runs: int
+    completed_runs: int
+    failed_runs: int
+    win_rate: float | None
+    avg_duration_days: float | None
+
+    # Runs by game
+    runs_by_game: list[GameRunCount]
+
+    # Encounter stats
+    total_encounters: int
+    caught_count: int
+    fainted_count: int
+    missed_count: int
+    catch_rate: float | None
+    avg_encounters_per_run: float | None
+
+    # Pokemon rankings
+    top_caught_pokemon: list[PokemonRanking]
+    top_encountered_pokemon: list[PokemonRanking]
+
+    # Team & deaths
+    total_deaths: int
+    mortality_rate: float | None
+    top_death_causes: list[DeathCause]
+    avg_catch_level: float | None
+    avg_faint_level: float | None
+    type_distribution: list[TypeCount]