fix(frontend): restore phase-gating build

frontend/src/api/client.ts

@@ -4,8 +4,8 @@ import {
   mapHealthResponse,
   mapJoinSessionResponse,
   mapMixAnswersResponse,
-  mapNextRoundResponse,
   mapScoreboardResponse,
+  mapStartNextRoundResponse,
   mapSessionDetailResponse,
   mapShowQuestionResponse,
   mapStartRoundResponse,
@@ -20,8 +20,8 @@ import type {
   JoinSessionRequest,
   JoinSessionResponse,
   MixAnswersResponse,
-  NextRoundResponse,
   ScoreboardResponse,
+  StartNextRoundResponse,
   SessionDetailResponse,
   ShowQuestionResponse,
   StartRoundRequest,
@@ -41,7 +41,7 @@ export interface ApiClient {
   mixAnswers(code: string, roundQuestionId: number): Promise<ApiResult<MixAnswersResponse>>;
   calculateScores(code: string, roundQuestionId: number): Promise<ApiResult<CalculateScoresResponse>>;
   getScoreboard(code: string): Promise<ApiResult<ScoreboardResponse>>;
-  startNextRound(code: string): Promise<ApiResult<NextRoundResponse>>;
+  startNextRound(code: string): Promise<ApiResult<StartNextRoundResponse>>;
   finishGame(code: string): Promise<ApiResult<FinishGameResponse>>;
   submitLie(code: string, roundQuestionId: number, payload: SubmitLieRequest): Promise<ApiResult<SubmitLieResponse>>;
   submitGuess(code: string, roundQuestionId: number, payload: SubmitGuessRequest): Promise<ApiResult<SubmitGuessResponse>>;
@@ -167,10 +167,10 @@ export function createApiClient(baseUrl = '', fetchImpl: typeof fetch = fetch):
         mapScoreboardResponse
       ),
     startNextRound: (code: string) =>
-      request<NextRoundResponse>(
+      request<StartNextRoundResponse>(
         `/lobby/sessions/${encodeURIComponent(normalizeCode(code))}/rounds/next`,
         'POST',
-        mapNextRoundResponse,
+        mapStartNextRoundResponse,
         {}
       ),
     finishGame: (code: string) =>

frontend/tests/vertical-slice.test.ts

@@ -56,7 +56,15 @@ function makeApiMock(overrides?: Partial<ApiClient>): ApiClient {
         session: { code: 'ABCD12', status: 'lie', current_round: 1 },
         round: { number: 1, category: { slug: 'history', name: 'History' } }
       }
-    })
+    }),
+    showQuestion: vi.fn(),
+    mixAnswers: vi.fn(),
+    calculateScores: vi.fn(),
+    getScoreboard: vi.fn(),
+    startNextRound: vi.fn(),
+    finishGame: vi.fn(),
+    submitLie: vi.fn(),
+    submitGuess: vi.fn()
   };
 
   return { ...base, ...overrides };