Python: Foundry hosting: update Responses agent history, options, and background #8744

Part of #8742. This is the Responses agent slice of the one-release redesign; its PR should close this child issue, not the umbrella. Depends on the trusted-scope foundation in #8743.

Deliverable

• Separate caller-facing Responses store/background from the developer's inner history choice: host transcript, downstream service storage, or an agent HistoryProvider. Keep downstream service_session_id private; outer response.id is the background polling handle. store=False must not write host-managed state or request inner provider storage.
• Translate applicable CreateResponse generation fields to MAF run options, then overlay flattened extra_body (extra values win translated-key collisions). Provide a developer hook to remove/replace caller options and configurable unsupported-option handling; leave agent defaults developer-owned. Reserve platform identity and continuation IDs from model options.
• Support request-owned agent factories and multi-turn steering/background with scoped persistence and clear failure behavior.

Compatibility

The deprecated history_source="agent" previously passed only new input and allowed the agent's own default to choose either an MAF history provider or downstream service storage. Do not silently remap it to inner_history="agent" in a way that forces store=False for a previously storing client. Keep old stored-request behavior or give an explicit, actionable conflict; warn once and document the explicit new mode. Keep store= as a deprecated constructor alias where feasible. The new caller store=False no-inner-storage rule still applies.

Review and validation

Ship responses/basic history/options/provider-background/client entry points, the steerable agent and local-tools samples with this implementation. Test stored/unstored foreground, background polls, provider-native background opt-in, streaming parity, option precedence and developer defaults, caller session_id filtering, and scoped conversation behavior. Do not include the native workflow API or workflow-only samples here.

The PR closing this issue should say Part of microsoft/agent-framework#8742; there is no intermediate package release. Related narrower work: #7389 (agent factories).