This moves the logic related to requesting and advertising addresses to
after the handshake completes as opposed to doing it during the
handshake in the version message handler.

In practice, the overall effect is the same, but moving it to happen
after the handshake has at least the following benefits:

- It helps ensure no other messages are queued up or sent between the
  version and verack messages
- It keeps the version handler focused on its primary purpose of
  negotiation and rejection of peers deemed to be unsuitable
- It is easier to reason about the sequence of events