I think it is important to distinguish between key exchange and digital signatures, as well as between protocol specifications and real-world deployments.
While IETF recommends hybrids for key exchange, that will likely not be the case for signatures. The Web is e.g., expected to use hybrid key exchange (X25519MLKEM768) together with standalone authentication (ML-DSA-44), which I think is a very sensible approach.
In practice, the right choice depends heavily on the use case, the protocol, the migration timeline, and your assessment of when a cryptographically relevant quantum computer (CRQC) will become available.
A good general recommendation is to use things that are already widely deployed whenever possible, as this maximizes implementation maturity. Conversely, if you believe nation-state adversaries will have access to CRQCs as early as 2029, deploying PQ/T hybrids
now provide little benefit and merely consume additional bandwidth, computation, and implementation complexity.
From a specification perspective, the most mature area is standalone signatures in X.509
From a deployment perspective, the most mature area is hybrid key exchange, which has already seen significant real-world deployment in TLS and SSH
Standalone post-quantum key exchange is somewhat less mature, while hybrid signatures remain the least mature.
I do not think any IETF protocol has fully migrated to PQC yet, that will likely take until 2035 or beyond.
One interesting protocol is LAKE, which defines a lightweight authenticated key exchange (AKE) protocol for constrained devices and low-bandwidth radio networks. More broadly, the IoT ecosystem encompasses a wide variety of deployment scenarios, each with very
different resource constraints. The size of ML-KEM and ML-DSA is a significant challenge for many constrained environments. LAKE has recently been rechartered to address post-quantum migration. In addition to signature-based authentication, the working group
has adopted work on KEM-based authentication. It has also identified the lack of lightweight post-quantum KEMs and NIKEs (non-interactive key exchange schemes) as a key challenge, and plans to ask CFRG to consider the specification of suitable lightweight
post-quantum key exchange algorithms. (LAKE has already standardized NIKE based authentication).
Another interesting protocol is MIKEY-SAKKE, which uses identity-based cryptography and currently has no straightforward migration path to post-quantum cryptography.
Cheers,
John Preuß Mattsson