Encryption migration gets most of the attention because of harvest-now-decrypt-later risk. Signatures have a different failure mode: if a quantum-capable attacker can forge a trusted signature, software updates, certificates, signed documents and identity assertions become harder to trust.
Signature migration is also operationally different from TLS key exchange. A signature can be stored, archived, countersigned, audited and verified years after it was created. That means the verifier population matters as much as the signing key.
The practical objective is crypto-agility: know where signatures are used, know how long they must remain trustworthy, and make sure signing and verification systems can accept NIST-standardised post-quantum options when the ecosystem is ready.