This issue is to capture the ux explorations for switching notebooks kernels/connections. These examples should consider connecting to a local server as well as a remote one. You can think of the relationship as servers (jupyter server) + databases (kernels).

Option A

This option shows local kernels by default and then provides an option to add a server. Once an additional server has been added, when the user attempts to switch kernels we'll show the parent (server) list first and then drill down to the kernels. If there is authentication (like in the Azure ML extension) then we'll use the authenticator provider.

Option B

This option also shows local kernels by default, but utilizes a custom view for managing connections. The user can switch kernels either from the quick pick or the view. Any kernel that the user connects to gets added to the respective list (similar to opening Recents quick pick).