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);
+  });
 });