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-frontend/e2e/server-operations.spec.ts

@@ -1176,20 +1176,29 @@ test('edits server reset defaults through profile metadata settings', async ({ p
     expect(request).toContain('"npcMode":2');
 });
 
-test('stores event season zero from server metadata settings', async ({ page }) => {
+test('stores event season zero and first game zero from server metadata settings', async ({ page }) => {
     const state: FixtureState = { operations: [], gatewayOperations: [], runtimeRunning: true, requestBodies: [] };
     await installFixture(page, state);
 
     await page.goto('admin/servers/che%3Adefault');
     const nextSeasonInput = page.getByTestId('next-season-idx');
+    const firstGameInput = page.getByTestId('first-game-idx');
     await nextSeasonInput.fill('0');
+    await firstGameInput.fill('0');
     await expect(nextSeasonInput).toHaveValue('0');
+    await expect(firstGameInput).toHaveValue('0');
     expect(
         await nextSeasonInput.evaluate((element: HTMLInputElement) => ({
             valid: element.validity.valid,
             valueAsNumber: element.valueAsNumber,
         }))
     ).toEqual({ valid: true, valueAsNumber: 0 });
+    expect(
+        await firstGameInput.evaluate((element: HTMLInputElement) => ({
+            valid: element.validity.valid,
+            valueAsNumber: element.valueAsNumber,
+        }))
+    ).toEqual({ valid: true, valueAsNumber: 0 });
     await page.getByPlaceholder('변경 사유 (필수)').fill('prepare event season');
     await page.getByRole('button', { name: '메타 저장' }).click();
 
@@ -1200,6 +1209,7 @@ test('stores event season zero from server metadata settings', async ({ page })
         state.requestBodies.find((entry) => entry.operation === 'admin.profiles.updateMeta')?.body
     );
     expect(request).toContain('"nextSeasonIdx":0');
+    expect(request).toContain('"firstGameIdx":0');
     await expect(page.getByTestId('action-toast').filter({ hasText: '메타 저장 완료' })).toBeVisible();
 });