New class to help reduce code duplication and centralize some EClient
handling policies.

Benefits:

- EClient instances can be shared across the entire application.

- Centralized rebroadcasting of "backend-died" and "backend-error"
  signals emitted from cached EClient instances.

- Automatic cache invalidation when backends crash.  The EClient
  is discarded, and a new instance is created on the next request.