Vault payment method stores the payment’s gateway token for the placed order with saving credit card information for the future.
The customer has placed an order from the site with checked Save Credit Card details for the next transaction from the Payment step, Vault store the gateway token for the Payment.
You can retrieve the payment Gateway token from the Order object.
Load the Order Object from the link, Get order data by order id Magento 2
Code Snippet to fetch Gateway Token from the Vault,
Using the above way, You can retrieve Gateway token from the Order.