[C++][FlightRPC] Refactor auth, middleware into the transport-agnostic layer

[asfimport]

A follow-up to ARROW-15282.

Reporter: David Li / @lidavidm

Related issues:

• [C++][FlightRPC] Support non-grpc data planes (relates to)
• [C++][FlightRPC] Refactor remaining methods into transport-agnostic handlers (is related to)
• [C++][FlightRPC] Implement a UCX transport (is related to)

_{Note: This issue was originally created as ARROW-15835. Please see the migration documentation for further details.}

[asfimport]

Todd Farmer / @toddfarmer:
This issue was last updated over 90 days ago, which may be an indication it is no longer being actively worked. To better reflect the current state, the issue is being unassigned. Please feel free to re-take assignment of the issue if it is being actively worked, or if you plan to start that work soon.