fix: polish authentication navigation and autofill

src/lib/api.ts

@@ -1,5 +1,6 @@
 import type * as Types from './types';
 import { apiBaseUrl } from '@/lib/site';
+import { AUTH_RETURN_TO_STORAGE_KEY, DEFAULT_AUTH_RETURN_TO, getSafeAuthReturnTo } from '@/lib/auth-return';
 
 const API_BASE_URL =
   apiBaseUrl;
@@ -221,8 +222,13 @@ class ApiClient {
     });
   }
 
-  async startGoogleLogin() {
+  async startGoogleLogin(returnTo = DEFAULT_AUTH_RETURN_TO) {
     if (typeof window !== 'undefined') {
+      try {
+        window.sessionStorage.setItem(AUTH_RETURN_TO_STORAGE_KEY, getSafeAuthReturnTo(returnTo));
+      } catch {
+        // The Google flow can still continue if session storage is unavailable.
+      }
       window.location.href = `${this.baseUrl}/api/auth/oauth/google/start`;
     }
   }