Magento2 Rest API Endpoint cmsPage rest/all/V1/cmsPage custom_layout_update property

Hello we are running a Magento 2.4.3 Store and want to roll out a fresh magento 2 instance with just one click.

For this purpose we have a set of static cms-pages that we want to deploy every time.

We are using the Rest API and the domain/rest/all/V1/cmsPage endpoint.

Everything works properly except the custom_layout_update_xml property. In previous magento2 versions there was a text-field for this purpose. I think as of Magento 2.3 or so this has changed to a dropdown field.

According to rest api there should be a string. We tried adding the filepath, the naming convention cms_page_view_selectable_faq_FAQ.xml, directly parse xml base64 and dropdown indexer like 0 or 1.

Example payload as suggested from the rest api:

{
  "page": {
    "id": 0,
    "identifier": "string",
    "title": "string",
    "page_layout": "string",
    "meta_title": "string",
    "meta_keywords": "string",
    "meta_description": "string",
    "content_heading": "string",
    "content": "string",
    "creation_time": "string",
    "update_time": "string",
    "sort_order": "string",
    "layout_update_xml": "string",
    "custom_theme": "string",
    "custom_root_template": "string",
    "custom_layout_update_xml": "string",
    "custom_theme_from": "string",
    "custom_theme_to": "string",
    "active": true
  }
}

Does anyone know what the required string here is?