feat(game): canonical gameId in POST /api/v1/admin/init

Engine no longer mints its own game UUID. The orchestrator (backend)
generates the game UUID at game-create time and passes it in the
admin/init request body as the required `gameId` field, so the value
that names the engine container and host bind-mount directory also
ends up inside the engine's state.json.

The engine rejects the zero UUID with 400 and any init that conflicts
with an existing state.json with 409 (a second init on the same gameId
is also a conflict; full idempotency is not part of the contract).

Updates rest.InitRequest, openapi.yaml (schema + 409 response),
controller.GenerateGame/NewGame/buildGameOnMap signatures, the engine
HTTP handler/executor, the backend runtime worker, and the relevant
unit and contract tests. Documentation in game/README.md,
docs/ARCHITECTURE.md, backend/README.md, and backend/docs/{runtime,flows}.md
is updated in the same patch.

Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>

game/openapi.yaml

@@ -69,8 +69,10 @@ paths:
       operationId: adminInitGame
       summary: Initialize a new game
       description: |
-        Generates a new game instance with the supplied list of races.
-        Requires at least 10 race entries. Routed only from the trusted
+        Generates a new game instance with the supplied canonical
+        `gameId` and list of races. Requires at least 10 race entries.
+        The engine refuses to overwrite an already-initialised storage
+        directory (responds with 409). Routed only from the trusted
         network segment that connects `Game Master` to the engine
         container.
       requestBody:
@@ -88,6 +90,8 @@ paths:
                 $ref: "#/components/schemas/StateResponse"
         "400":
           $ref: "#/components/responses/ValidationError"
+        "409":
+          $ref: "#/components/responses/ConflictError"
         "500":
           $ref: "#/components/responses/InternalError"
   /api/v1/admin/race/banish:
@@ -410,10 +414,23 @@ components:
           description: True when the race has been eliminated or voluntarily quit.
     InitRequest:
       type: object
-      description: Initialization request specifying the race list for a new game.
+      description: |
+        Initialization request specifying the canonical game identity
+        and the race list for a new game. `gameId` is generated by the
+        orchestrator (the platform's backend) before the engine
+        container is launched; the engine rejects the zero UUID and
+        any value that conflicts with an existing `state.json` on
+        disk.
       required:
+        - gameId
         - races
       properties:
+        gameId:
+          type: string
+          format: uuid
+          description: |
+            Canonical game identity supplied by the orchestrator. Must
+            be a non-zero UUID.
         races:
           type: array
           description: List of participating races. Minimum 10 entries required.
@@ -1299,6 +1316,19 @@ components:
         error:
           type: string
           description: Human-readable validation error message from the binding layer.
+    ConflictErrorResponse:
+      type: object
+      description: |
+        Conflict error returned when the engine refuses an operation
+        that would clash with persisted state. Today the only producer
+        is `POST /api/v1/admin/init` when the storage directory
+        already contains a game state.
+      required:
+        - error
+      properties:
+        error:
+          type: string
+          description: Human-readable conflict description.
     InternalErrorResponse:
       type: object
       description: |
@@ -1326,6 +1356,17 @@ components:
             validationError:
               value:
                 error: "Key: 'InitRequest.Races' Error:Field validation for 'Races' failed on the 'gte' tag"
+    ConflictError:
+      description: |
+        The requested operation conflicts with persisted engine state.
+      content:
+        application/json:
+          schema:
+            $ref: "#/components/schemas/ConflictErrorResponse"
+          examples:
+            alreadyInitialized:
+              value:
+                error: "game init: game already initialized"
     InternalError:
       description: Internal Game Service error.
       content: