who is the 3rd part company that Apple uses to store our credit cards in the Apple Wallet

Apple doesn’t use a third party. You have data stored on your iPhone in the Secure Enclave. The data that is stored there is encrypted and Apple does not have the key. Apple also stores encrypted data on its servers. You bank has the decrypted data and the key to decrypt the data Apple sends. There are other processes involved, but the data is always encrypted.

Some banks may use an external company for account verification. This could be a company that offers merchant services or the Payment Network (Visa, Mastercard, Discover, American Express etc.).

You might find this blog post informative.

https://codeburst.io/how-does-apple-pay-actually-work-f52f7d9348b7

It’s fairly technical, but you’ll see that once setup, Apple is “out of the loop.”

At that point it’s all between your phone, your issuer, and the respective processing network entities.