fix(cliproxy): preserve kiro paste-callback start route

tests/unit/cliproxy/auth-types-management-path.test.ts

@@ -1,22 +1,30 @@
 import { describe, expect, it } from 'bun:test';
 import {
   getManagementAuthUrlPath,
+  getPasteCallbackStartPath,
   getManagementOAuthCallbackPath,
 } from '../../../src/cliproxy/auth/auth-types';
 
-describe('auth-types management auth-url path', () => {
+describe('auth-types paste-callback start path', () => {
   it('maps providers to CLIProxyAPI management auth-url routes', () => {
-    expect(getManagementAuthUrlPath('gemini')).toBe(
+    expect(getPasteCallbackStartPath('gemini')).toBe(
       '/v0/management/gemini-cli-auth-url?is_webui=true'
     );
-    expect(getManagementAuthUrlPath('codex')).toBe('/v0/management/codex-auth-url?is_webui=true');
-    expect(getManagementAuthUrlPath('agy')).toBe(
+    expect(getPasteCallbackStartPath('codex')).toBe('/v0/management/codex-auth-url?is_webui=true');
+    expect(getPasteCallbackStartPath('agy')).toBe(
       '/v0/management/antigravity-auth-url?is_webui=true'
     );
-    expect(getManagementAuthUrlPath('claude')).toBe(
+    expect(getPasteCallbackStartPath('claude')).toBe(
       '/v0/management/anthropic-auth-url?is_webui=true'
     );
-    expect(getManagementAuthUrlPath('ghcp')).toBe('/v0/management/github-auth-url?is_webui=true');
+    expect(getPasteCallbackStartPath('ghcp')).toBe('/v0/management/github-auth-url?is_webui=true');
+  });
+
+  it('keeps Kiro on the legacy start route for paste-callback mode', () => {
+    expect(getPasteCallbackStartPath('kiro')).toBe('/oauth/kiro/start');
+  });
+
+  it('still exposes the generic management auth-url helper', () => {
     expect(getManagementAuthUrlPath('kiro')).toBe('/v0/management/kiro-auth-url?is_webui=true');
   });