Could you please advise on any additional settings or requirements needed to populate the key selection dropdown?

According to this MS-Document,

As far as I know, you can't authenticate with Azure Key Vault when creating an Azure SFTP local user.

First create SSH key from Azure portal through this MS-Document.

Once you've created the SSH key through the Azure portal, you will now be able to see the key under Use existing key stored in Azure.

Portal: