With Sigstore, they perform an OIDC flow against an identity provider: that results in a verifiable identity credential, which is then bound to a short-lived (~15m) signing key that produces the signatures. That signing key is simultaneously attested through a traditional X.509 PKI (it gets a certificate, that certificate is uploaded to an append-only transparency log, etc.).
So: in the normal flow, the user never directly specifies the cryptographic key -- the scheme ensures that they have a strong, ephemeral one generated for them on the spot (and only on their client device, in RAM). That key gets bound to their long-lived identity, so verifiers don't need to know which key they're verifying; they only need to determine whether they trust the identity itself (which can be an email address, a GitHub repository, etc.).
Serverside TUF keys are implemented FWICS, but clientside digital publisher signatures (like e.g. MS Windows .exe's have had when you view the "Properties" of the file for many years now) are not yet implemented.
Hopefully I'm just out of date.