Is your feature request related to a problem? Please describe.
from_connection_string is a core component of our APIs, both the ServiceBusClient and ServiceBusAdministrationClient. However, we currently have two distinct implementations, which while very similar are not quite aligned.
(see breadcrumb here)

Describe the solution you'd like
Understand the difference between the two, (Sync with @YijunXieMS if needed for history on why the management client is distinct, if any specific impetus went into that) and unify.

Describe alternatives you've considered
The only real alternative here is keeping them separate. If something is discovered in this process that indicates they should not be unified, am open to that, but would be very curious.