fix(oauth): persist successful login status across navigation

tests/oauthLoginState.test.ts

@@ -0,0 +1,22 @@
+import { describe, expect, test } from 'bun:test';
+import {
+  createOAuthLoginSuccessCache,
+  shouldShowOAuthLoginStatus,
+} from '../src/services/oauthLoginState';
+
+describe('OAuth login display state', () => {
+  test('only successful login states display a status badge', () => {
+    expect(shouldShowOAuthLoginStatus('idle')).toBeFalse();
+    expect(shouldShowOAuthLoginStatus('waiting')).toBeFalse();
+    expect(shouldShowOAuthLoginStatus('error')).toBeFalse();
+    expect(shouldShowOAuthLoginStatus('success')).toBeTrue();
+  });
+
+  test('successful providers remain cached across page remounts', () => {
+    const cache = createOAuthLoginSuccessCache<'codex' | 'claude'>();
+    cache.mark('codex');
+
+    expect(cache.snapshot()).toEqual(['codex']);
+    expect(cache.snapshot()).toEqual(['codex']);
+  });
+});