Add game category and region metadata for genlocke presets

Add `category` field (original/remake/enhanced/sequel/spinoff) to the
Game model and tag all 38 games. Create regions.json with generation
mapping, ordering, and genlocke preset defaults per region. Add
GET /games/by-region endpoint returning games grouped by region.

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

backend/src/app/schemas/game.py

@@ -17,6 +17,7 @@ class GameResponse(CamelModel):
     slug: str
     generation: int
     region: str
+    category: str | None = None
     box_art_url: str | None
     release_year: int | None
     color: str | None
@@ -39,6 +40,7 @@ class GameCreate(CamelModel):
     slug: str
     generation: int
     region: str
+    category: str | None = None
     box_art_url: str | None = None
     release_year: int | None = None
     color: str | None = None
@@ -49,11 +51,25 @@ class GameUpdate(CamelModel):
     slug: str | None = None
     generation: int | None = None
     region: str | None = None
+    category: str | None = None
     box_art_url: str | None = None
     release_year: int | None = None
     color: str | None = None
 
 
+class GenlockeDefaultsResponse(CamelModel):
+    true_genlocke: str  # game slug for true genlocke default
+    normal_genlocke: str  # game slug for normal genlocke default
+
+
+class RegionResponse(CamelModel):
+    name: str
+    generation: int
+    order: int
+    genlocke_defaults: GenlockeDefaultsResponse
+    games: list[GameResponse] = []
+
+
 class RouteCreate(CamelModel):
     name: str
     order: int