fix: route Cursor auth through browser polling

Closes #1194

tests/unit/ui/provider-config.test.ts

@@ -2,6 +2,7 @@ import { describe, expect, it } from 'bun:test';
 import {
   getDeviceCodeProviderInstruction,
   getProviderDisplayName,
+  isDeviceCodeProvider,
 } from '../../../ui/src/lib/provider-config';
 
 describe('provider-config fallbacks', () => {
@@ -15,4 +16,10 @@ describe('provider-config fallbacks', () => {
       'Complete the authorization in your browser.'
     );
   });
+
+  it('does not classify Cursor browser URL auth as a verification-code device flow', () => {
+    expect(isDeviceCodeProvider('cursor')).toBe(false);
+    expect(isDeviceCodeProvider('ghcp')).toBe(true);
+    expect(isDeviceCodeProvider('qwen')).toBe(true);
+  });
 });

tests/unit/web-server/cliproxy-auth-routes-manual-callback.test.ts

@@ -11,7 +11,7 @@ import {
   getCachedQuota,
   setCachedQuota,
 } from '../../../src/cliproxy/quota/quota-response-cache';
-import { restoreFetch, mockFetch } from '../../mocks';
+import { restoreFetch, mockFetch, getCapturedFetchRequests } from '../../mocks';
 
 describe('cliproxy-auth-routes manual callback nickname persistence', () => {
   let server: Server;
@@ -179,6 +179,34 @@ describe('cliproxy-auth-routes manual callback nickname persistence', () => {
     expect(registry.providers.kiro.accounts['github-ABC123']?.nickname).toBe('work');
   });
 
+  it('starts Cursor auth through the browser URL management endpoint', async () => {
+    mockFetch([
+      {
+        url: /\/v0\/management\/cursor-auth-url\?is_webui=true$/,
+        response: {
+          url: 'https://cursor.com/loginDeepControl?state=cursor-state',
+          state: 'cursor-state',
+        },
+      },
+    ]);
+
+    const startResponse = await postJson('/api/cliproxy/auth/cursor/start-url', {
+      nickname: 'work',
+    });
+
+    expect(startResponse.status).toBe(200);
+    expect(startResponse.body).toEqual({
+      success: true,
+      authUrl: 'https://cursor.com/loginDeepControl?state=cursor-state',
+      state: 'cursor-state',
+      method: null,
+    });
+
+    const requests = getCapturedFetchRequests();
+    expect(requests).toHaveLength(1);
+    expect(requests[0]?.url).toContain('/v0/management/cursor-auth-url?is_webui=true');
+  });
+
   it('returns wait after callback submission when the local token is not yet available', async () => {
     mockFetch([
       {

tests/unit/web-server/cliproxy-auth-routes.test.ts

@@ -13,15 +13,14 @@ describe('cliproxy-auth-routes start-url guard', () => {
     );
     expect(getStartUrlUnsupportedReason('ghcp')).toContain("Provider 'ghcp' uses Device Code flow");
     expect(getStartUrlUnsupportedReason('qwen')).toContain("Provider 'qwen' uses Device Code flow");
-    expect(getStartUrlUnsupportedReason('cursor')).toContain(
-      "Provider 'cursor' uses Device Code flow"
-    );
     expect(getStartUrlUnsupportedReason('codebuddy')).toContain(
       "Provider 'codebuddy' uses Device Code flow"
     );
-    expect(getStartUrlUnsupportedReason('kilo')).toContain(
-      "Provider 'kilo' uses Device Code flow"
-    );
+    expect(getStartUrlUnsupportedReason('kilo')).toContain("Provider 'kilo' uses Device Code flow");
+  });
+
+  it('allows Cursor browser URL auth on start-url', () => {
+    expect(getStartUrlUnsupportedReason('cursor')).toBeNull();
   });
 
   it('allows Kiro social methods on start-url', () => {
@@ -138,6 +137,8 @@ describe('cliproxy-auth-routes nickname validation', () => {
     ];
 
     expect(getStartAuthNicknameError('kiro', 'work', existingAccounts, 'github-ABC123')).toBeNull();
-    expect(getStartAuthNicknameError('kiro', 'github-ABC123', existingAccounts, 'github-ABC123')).toBeNull();
+    expect(
+      getStartAuthNicknameError('kiro', 'github-ABC123', existingAccounts, 'github-ABC123')
+    ).toBeNull();
   });
 });