Azure also offers Managed HSM that are FIPS 140-2 lvl 3 compliant.
These instances follow the AKV API (no secret & cert support)

It would be nice to have the option to also use managed.
Managed HSM should support the action: getKey & signKey

The only difference is, that they use a different default endpoint: <your-HSM-name>.managedhsm.azure.net

Maybe that could be supported by setting a new optional flag within the uri parameter. E.g. managedhsm=true, or hsm=premium|managed|dedicated

premium = Current behavior using Premium AKV
managed = using Azure Managed HSM
dedicated = future implementation to support dedicated Azure HSM instances

See for a comparison of different AKV SKU