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/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