API: Refactor continuation code and add to purge, watch, etc.

API: Refactor continuation code and add to purge, watch, etc.

While generator support was added to various actions, the continuation
parameters from the generators weren't being returned to the client.

This patch refactors the code for handling continuation out of ApiQuery
and into ApiResult, and then uses it in the other actions that need it.

Bug: 60734
Change-Id: I1a6e51cdc964ddcdd69aaa2f735223371233e8af