Update homepage routes to include language and mode

apps/homepage/src/components/auth/ResetPasswordForm.tsx

@@ -4,8 +4,8 @@ import { Button } from '@/components/actions/Button';
 import { FormField } from '@/components/forms/FormField';
 import { AuthShell } from '@/components/auth/AuthShell';
 import { API_BASE } from '@/lib/api';
-import { localizedPath, type Locale } from '@/lib/localization/config';
-import { useSearchParams } from 'next/navigation';
+import { localizedModePath, modeFromPathname, type Locale } from '@/lib/localization/config';
+import { usePathname, useSearchParams } from 'next/navigation';
 import { Suspense, useState } from 'react';
 import styles from './AuthForms.module.css';
 
@@ -88,6 +88,7 @@ const dicts: Record<string, Dict> = {
 function ResetPasswordContent({ locale }: { locale: Locale }) {
   const dict = (dicts[locale] ?? dicts.en) as Dict;
   const searchParams = useSearchParams();
+  const mode = modeFromPathname(usePathname());
   const token = searchParams.get('token');
 
   const [password, setPassword] = useState('');
@@ -139,8 +140,8 @@ function ResetPasswordContent({ locale }: { locale: Locale }) {
     }
   }
 
-  const signInHref = localizedPath('sign-in', locale);
-  const forgotHref = localizedPath('forgot-password', locale);
+  const signInHref = localizedModePath('sign-in', locale, mode);
+  const forgotHref = localizedModePath('forgot-password', locale, mode);
 
   if (!token) {
     return (