feat: add frontend API clients for branches, handoffs, and resolutions

Adds branchesApi (getBranches, createFork, updateBranchStatus, switchBranch,
reviveBranch, sendBranchMessage), handoffsApi (createHandoff, listHandoffs,
claimHandoff, getQueue), and resolutionsApi (getOutputs, editOutput, pushOutput).
All exported from api/index.ts.

Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>

frontend/src/api/handoffs.ts

@@ -0,0 +1,39 @@
+import apiClient from './client'
+import type {
+  HandoffCreateRequest,
+  HandoffResponse,
+  QueueItemResponse,
+} from '@/types/branching'
+
+export const handoffsApi = {
+  async createHandoff(sessionId: string, data: HandoffCreateRequest): Promise<HandoffResponse> {
+    const response = await apiClient.post<HandoffResponse>(
+      `/ai-sessions/${sessionId}/handoff`,
+      data
+    )
+    return response.data
+  },
+
+  async listHandoffs(sessionId: string): Promise<HandoffResponse[]> {
+    const response = await apiClient.get<HandoffResponse[]>(
+      `/ai-sessions/${sessionId}/handoffs`
+    )
+    return response.data
+  },
+
+  async claimHandoff(handoffId: string): Promise<HandoffResponse> {
+    const response = await apiClient.post<HandoffResponse>(
+      `/handoffs/${handoffId}/claim`
+    )
+    return response.data
+  },
+
+  async getQueue(params?: { intent?: 'park' | 'escalate'; limit?: number }): Promise<QueueItemResponse[]> {
+    const response = await apiClient.get<QueueItemResponse[]>('/handoffs/queue', {
+      params,
+    })
+    return response.data
+  },
+}
+
+export default handoffsApi