feat(gateway): 프로필별 첫 기수 번호를 관리한다

첫 기수 번호를 완료 게임 수의 기준값으로 적용하고 0기를 API와 화면에서 보존한다. 시즌 번호와 독립된 RESET 계약을 관리 패널, 테스트, 운영 문서에 반영한다.

app/gateway-api/test/adminOperations.test.ts

@@ -877,6 +877,30 @@ describe('admin operation API', () => {
         ).rejects.toBeDefined();
     });
 
+    it('stores zero as the first game index and rejects negative values', async () => {
+        const harness = await buildCaller(
+            async () => {
+                throw new Error('not used');
+            },
+            { adminRoles: ['admin.profiles.settings:che:2'], firstUserIsAdmin: false }
+        );
+
+        await harness.caller.admin.profiles.updateMeta({
+            profileName: 'che:2',
+            patch: { firstGameIdx: 0 },
+            reason: 'start core series at zero',
+        });
+        expect(harness.updatedMetas.at(-1)).toMatchObject({ firstGameIdx: 0 });
+
+        await expect(
+            harness.caller.admin.profiles.updateMeta({
+                profileName: 'che:2',
+                patch: { firstGameIdx: -1 },
+                reason: 'reject negative game index',
+            })
+        ).rejects.toBeDefined();
+    });
+
     it('does not let a scenario-only operator combine a Git update with reset', async () => {
         const harness = await buildCaller(
             async () => {

app/gateway-api/test/profileGameIndex.test.ts

@@ -0,0 +1,16 @@
+import { describe, expect, it } from 'vitest';
+
+import { resolveProfileFirstGameIdx } from '../src/orchestrator/gatewayOrchestrator.js';
+
+describe('profile first game index', () => {
+    it('preserves an explicitly configured zero', () => {
+        expect(resolveProfileFirstGameIdx({ firstGameIdx: 0 })).toBe(0);
+    });
+
+    it('defaults missing or invalid metadata to one', () => {
+        expect(resolveProfileFirstGameIdx({})).toBe(1);
+        expect(resolveProfileFirstGameIdx({ firstGameIdx: -1 })).toBe(1);
+        expect(resolveProfileFirstGameIdx({ firstGameIdx: 0.5 })).toBe(1);
+        expect(resolveProfileFirstGameIdx({ firstGameIdx: 'invalid' })).toBe(1);
+    });
+});

app/gateway-api/test/profileSeedCli.integration.test.ts

@@ -41,6 +41,8 @@ describeDatabase('selected workspace profile seed CLI', () => {
         const requestFile = path.join(tempDirectory, 'request.json');
         const connector = createGamePostgresConnector({ url: databaseUrl });
         try {
+            await connector.connect();
+            const completedGameCount = await connector.prisma.gameHistory.count({ where: { status: 'COMPLETED' } });
             await fs.writeFile(
                 requestFile,
                 JSON.stringify({
@@ -49,6 +51,7 @@ describeDatabase('selected workspace profile seed CLI', () => {
                     now: '2036-03-03T00:00:00.000Z',
                     installOptions: {
                         serverId: 'selected-cli-seed',
+                        firstGameIdx: 0,
                         installOperationId: 'selected-cli-operation',
                         installCommitSha: 'selected-cli-commit',
                     },
@@ -63,11 +66,12 @@ describeDatabase('selected workspace profile seed CLI', () => {
 
             const result = await runSeedCli(requestFile);
             expect(result, result.output).toMatchObject({ code: 0 });
-            await connector.connect();
             const world = await connector.prisma.worldState.findFirstOrThrow();
             expect(world).toMatchObject({
                 scenarioCode: '1010',
                 meta: {
+                    firstGameIdx: 0,
+                    gameIdx: completedGameCount,
                     installOperationId: 'selected-cli-operation',
                     installCommitSha: 'selected-cli-commit',
                 },