Custom Field in Custom account tab not saving

Hello,
According to the UM sample to add a member Account Tab there :
https://docs.ultimatemember.com/article/65-extend-ultimate-member-account-page-with-custom-tabs-content

I have created custom fields on a UM Form (not displayed in any other part of the website), and then I have managed to display them into the tab by adding the following code after the <!– Here goes your custom content –>

    global $ultimatemember;
    $id = um_user('ID');
     $names = [ 'pilot_total_hours','pilot_hours_cdb','pilot_hours_cdb_last_year','pilot_hours_cdb_3months','pilot_hours_since_ppl'];
    
    $fields = [];
    foreach($names as $name)
       	$fields[$name] = UM()->builtin()->get_specific_field($name);
    
    $fields = apply_filters('um_account_secure_fields', $fields, get_current_user_id());

    foreach( $fields as $key => $data )
       	$output2 .= UM()->fields()->edit_field( $key, $data );

    echo str_ireplace("\\", "", $output2);

This display properly the form with fields and labels, etc BUT values are not saved despite the green message telling that profile has been updated.

What is missing on my code ?