An attestation certificate is automatically generated for all public keys when you generate the key pair. If you use the Smart Card Shell to generate a key, then you can see the attestation certificate linked to the private key.
The attestation is actually an authenticated card verifiable certificate request (CSR) as defined in the BSI TR 03110, which is the basis of the EAC PKI used in passports and national eID cards. The CSR is signed by the device authentication key, which is certified by the Device Issuer CA, which is ultimately signed by the Scheme Root CA.
The CSR (we usually call the structure authenticated public key) is also used in the public key authentication, authenticated key derivation and XKEK key domain management. So it’s a quite universal mechanism in the SmartCard-HSM.