Add REST API endpoints for games, runs, and encounters

Implement 13 endpoints: read-only reference data (games, routes, pokemon),
run CRUD with cascading deletes, and encounter management. Uses Pydantic v2
with camelCase alias generation to match frontend types, and nested response
schemas for detail views.

Co-Authored-By: Claude Opus 4.5 <noreply@anthropic.com>

backend/src/app/api/games.py

@@ -0,0 +1,50 @@
+from fastapi import APIRouter, Depends, HTTPException
+from sqlalchemy import select
+from sqlalchemy.ext.asyncio import AsyncSession
+from sqlalchemy.orm import selectinload
+
+from app.core.database import get_session
+from app.models.game import Game
+from app.models.route import Route
+from app.schemas.game import GameDetailResponse, GameResponse, RouteResponse
+
+router = APIRouter()
+
+
+@router.get("", response_model=list[GameResponse])
+async def list_games(session: AsyncSession = Depends(get_session)):
+    result = await session.execute(select(Game).order_by(Game.id))
+    return result.scalars().all()
+
+
+@router.get("/{game_id}", response_model=GameDetailResponse)
+async def get_game(game_id: int, session: AsyncSession = Depends(get_session)):
+    result = await session.execute(
+        select(Game)
+        .where(Game.id == game_id)
+        .options(selectinload(Game.routes))
+    )
+    game = result.scalar_one_or_none()
+    if game is None:
+        raise HTTPException(status_code=404, detail="Game not found")
+
+    # Sort routes by order for the response
+    game.routes.sort(key=lambda r: r.order)
+    return game
+
+
+@router.get("/{game_id}/routes", response_model=list[RouteResponse])
+async def list_game_routes(
+    game_id: int, session: AsyncSession = Depends(get_session)
+):
+    # Verify game exists
+    game = await session.get(Game, game_id)
+    if game is None:
+        raise HTTPException(status_code=404, detail="Game not found")
+
+    result = await session.execute(
+        select(Route)
+        .where(Route.game_id == game_id)
+        .order_by(Route.order)
+    )
+    return result.scalars().all()