How to Retrieve Subscription Details for Orders Using Shopify REST API

Hi - this may be easier to achieve with the GraphQL API rather than the REST API. There is a subscriptionContract query on the GraphQL API which you could use to get info about a subscription contract that is associated with an order, it could look something like this:

query GetSubscriptionContractDetails {
  subscriptionContract(id: "gid://shopify/SubscriptionContract/1234567890") {
    id
    nextBillingDate
    status
    deliveryPolicy {
      interval
      intervalCount
    }
    customer {
      id
      email
      displayName
    }
    lines(first: 50, reverse: true) {
      edges {
        node {
          productId
          currentPrice {
            amount
            currencyCode
          }
          quantity
          title
          variantTitle
        }
      }
    }
    orders(first: 1, reverse: true) {
      edges {
        node {
          id
        }
      }
    }
  }
}