How do I update user email from frontend input field?

by

You can diagnose error while updating user email.

$user_data = wp_update_user( array( 'ID' => $user_id, 'user_email' => $email ) );
 
if ( is_wp_error( $user_data ) ) {
    // There was an error; possibly this user doesn't exist.
    echo 'Error.';
} else {
    // Success!
    echo 'User profile updated.';
}

Might it can help you.