The bulk of the change here is making the naming and contents of the
conversion to/from Responses API inputs -> Chat Completion API
messages and Chat Completion API choices -> Responses API outputs more
clear with some code comments, method renaming, and slight
refactoring.
There are also some other minor changes, like moving a pydantic model
from the api/ to the implementation since it's not actually exposed
via the API, as well as making some if/else usage more clear.
Signed-off-by: Ben Browning <bbrownin@redhat.com>