Getting Pages via API ... Liquid template configuration?

[greekTRUE]

I've gotten pages from the Storefront API via a query like this one:

query {
  pages(first:5) {
    edges {
      node {
        handle
        body
        createdAt
        bodySummary
      }
    }
  }
}

 ...but I can see from the documentation page:

https://shopify.dev/api/storefront/reference/online-store/page

...that there's no information about which Liquid template the page is using. I have a client who has liquid templates on their previously existing pages, and we need to know which ones to determine how to properly render the page on the headless site.

Is there any way to figure out which template a page is configured to use? Maybe with the admin API? If not, is this a feature you have considered adding in the future?