The issuer puts the holder's public key into the credential (cnf.jwk in SD-JWT; the device key in an mdoc's mobile security object). At presentation the holder signs a fresh, verifier-specific challenge: SD-JWT uses a JWT with typ kb+jwt, aud, nonce, iat and sd_hash (RFC 9901 §4.3); mdoc signs or MACs the session transcript (ISO/IEC 18013-5). Verifiers check the nonce and audience to stop replay to another verifier.
Key binding is only as good as the protection of the holder key, which is why wallets keep it in secure hardware and why issuers ask for wallet or key attestations before issuing. The same idea appears in OAuth as sender-constrained tokens (DPoP, mTLS).