[Common Recorder] Update the KeyVault packages to use the latest API

[sadasant]

Follow the list here: #4229

[ramya-rao-a]

@sadasant Can you clarify which API are we referring to here when we say "Update the KeyVault packages to use the latest API"?

Also, when you say "Follow the list here: #4229", do you mean the entire list there or just the below?

cc @jonathandturner

[sadasant]

It's all of it. The keyvault packages have a recorder that remains from the older code we had. It also has references to methods to obtain unique strings and delays. The recorder now has some of this, but I want to make sure that it addresses what we address in KeyVault. I haven't wanted to do that preemptively because I think there's not a perfect overlap. I will clean this up, for sure.

[ramya-rao-a]

Closing in favor of #6300