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/branches.ts

@@ -0,0 +1,67 @@
+import apiClient from './client'
+import type {
+  BranchTreeResponse,
+  ForkCreateRequest,
+  ForkPointResponse,
+  BranchSwitchResponse,
+  ReviveRequest,
+  BranchMessageRequest,
+  BranchMessageResponse,
+} from '@/types/branching'
+
+export const branchesApi = {
+  async getBranches(sessionId: string): Promise<BranchTreeResponse> {
+    const response = await apiClient.get<BranchTreeResponse>(
+      `/ai-sessions/${sessionId}/branches`
+    )
+    return response.data
+  },
+
+  async createFork(sessionId: string, data: ForkCreateRequest): Promise<ForkPointResponse> {
+    const response = await apiClient.post<ForkPointResponse>(
+      `/ai-sessions/${sessionId}/branches/fork`,
+      data
+    )
+    return response.data
+  },
+
+  async updateBranchStatus(
+    sessionId: string,
+    branchId: string,
+    status: string,
+    reason?: string
+  ): Promise<void> {
+    await apiClient.patch(
+      `/ai-sessions/${sessionId}/branches/${branchId}/status`,
+      { status, reason }
+    )
+  },
+
+  async switchBranch(sessionId: string, branchId: string): Promise<BranchSwitchResponse> {
+    const response = await apiClient.post<BranchSwitchResponse>(
+      `/ai-sessions/${sessionId}/branches/${branchId}/switch`
+    )
+    return response.data
+  },
+
+  async reviveBranch(sessionId: string, branchId: string, data: ReviveRequest): Promise<void> {
+    await apiClient.post(
+      `/ai-sessions/${sessionId}/branches/${branchId}/revive`,
+      data
+    )
+  },
+
+  async sendBranchMessage(
+    sessionId: string,
+    branchId: string,
+    data: BranchMessageRequest
+  ): Promise<BranchMessageResponse> {
+    const response = await apiClient.post<BranchMessageResponse>(
+      `/ai-sessions/${sessionId}/branches/${branchId}/message`,
+      data
+    )
+    return response.data
+  },
+}
+
+export default branchesApi

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

frontend/src/api/index.ts

@@ -32,3 +32,6 @@ export { publicTemplatesApi } from './publicTemplates'
 export { uploadsApi, default as uploadsApiDefault } from './uploads'
 export { scriptBuilderApi } from './scriptBuilder'
 export { betaFeedbackApi } from './betaFeedback'
+export { branchesApi } from './branches'
+export { handoffsApi } from './handoffs'
+export { resolutionsApi } from './resolutions'

frontend/src/api/resolutions.ts

@@ -0,0 +1,42 @@
+import apiClient from './client'
+import type {
+  AllResolutionOutputsResponse,
+  ResolutionOutputResponse,
+  ResolutionOutputEditRequest,
+  ResolutionOutputPushRequest,
+} from '@/types/branching'
+
+export const resolutionsApi = {
+  async getOutputs(sessionId: string): Promise<AllResolutionOutputsResponse> {
+    const response = await apiClient.get<AllResolutionOutputsResponse>(
+      `/ai-sessions/${sessionId}/resolution-outputs`
+    )
+    return response.data
+  },
+
+  async editOutput(
+    sessionId: string,
+    outputId: string,
+    data: ResolutionOutputEditRequest
+  ): Promise<ResolutionOutputResponse> {
+    const response = await apiClient.patch<ResolutionOutputResponse>(
+      `/ai-sessions/${sessionId}/resolution-outputs/${outputId}`,
+      data
+    )
+    return response.data
+  },
+
+  async pushOutput(
+    sessionId: string,
+    outputId: string,
+    data: ResolutionOutputPushRequest
+  ): Promise<ResolutionOutputResponse> {
+    const response = await apiClient.post<ResolutionOutputResponse>(
+      `/ai-sessions/${sessionId}/resolution-outputs/${outputId}/push`,
+      data
+    )
+    return response.data
+  },
+}
+
+export default resolutionsApi