As you've found when a customer goes through the Shopify checkout process and the system reaches out to the Carrier Service for shipping rates, the data included in the requests are typically related to the order itself (e.g., order contents, destination address) rather than information about the customer who is placing the order - which is why you're not seeing data like `customer_id`.
As a work around, you could potentially store customer-specific shipping rules in a metafield (or a separate system) based on the customer ID, and then use that information when generating shipping rates within your app. However, this would not involve the Carrier Service API directly.
Here's an general approach on how it could work:
When a customer logs in or otherwise interacts with your storefront, you can use the Storefront API or Admin API to fetch their customer ID and any other necessary information. This might be based on their tags, customer group, or other criteria.