The current implementation of sessions saves the session on the final output. This works as a "memory" of previous full conversations, but does not work if you need access to the session during the turn. A use case for this is providing access to the full conversation to an agent-as-tool during the turn.

This PR updates the run and _start_streaming methods in run.py to save the session on each turn.

The basic flow is:

• On completion start, save the input into the session.
• After each turn, add only the turn results to the session.

Also included is an example file that shows the use of this pattern. It is an adapted version of the agents-as-tools example where a check agent is called within the same turn as the translation agents and examines their outputs via the conversation history, rather than as a generated input.

• Current tests pass and I don't think an update to the tests is needed for this PR.
• Documentation about sessions did not cover this case, but I felt it was implied that it would work. I think these changes bring the behavior in line with the documentation.
• I have added an example that demonstrates it in action.