Azure Auth config parsing migration to extensions

Maybe in the future, we can hand some of this app.config parsing off to the azure package. That should break some of the coupling we're getting here.

_Originally posted by @mdaigle in https://github.com/dotnet/SqlClient/pull/4288#discussion_r3438985220_

Start by locating the current app.config parsing and the related Azure authentication configuration. Read how the Azure package exposes extensions and determine whether this parsing can be handed off there. Done means the coupling is reduced and Azure authentication configuration continues to work through the extension-based path.

Written by the indexing model from the issue text.