Python: Fix Responses API handoff state handling and add focused tests

[alliscode]

This pull request addresses critical issues with agent handoff behavior when using Responses API-style clients, ensuring conversation context and session state are correctly managed across handoffs. It introduces regression tests to verify these invariants and updates the orchestration logic to prevent context loss and stale session IDs that could cause API errors.

Bug fixes for handoff and session management:

• Ensured the agent receives the full conversation history (_full_conversation) as input after a handoff, rather than just the latest broadcast, to preserve context for APIs like the Responses API.
• Cleared the session's service_session_id after a handoff to prevent sending a stale previous_response_id, which could otherwise cause "No tool output found" errors with the Responses API.

Testing and regression coverage:

• Added a new test suite (test_handoff_responses.py) with regression tests to verify that (1) handoffs correctly clear the session's conversation pointer and (2) agents receive the complete conversation context after a handoff. This includes a mock client and agent simulating Responses API behavior.

Closes #4053

Contribution Checklist

• The code builds clean without any errors or warnings
• The PR follows the Contribution Guidelines
• All unit tests pass, and I have added new tests where possible
• Is this a breaking change? If yes, add "[BREAKING]" prefix to the title of the PR.

[markwallace-microsoft]

Python Test Coverage Report •

File	Stmts	Miss	Cover	Missing
packages/orchestrations/agent_framework_orchestrations
_handoff.py	342	57	83%	105–106, 108, 163–173, 175, 177, 179, 184, 282, 335, 360, 402–403, 417, 475–476, 508, 514, 518, 522–523, 561–563, 568–570, 686, 689, 696, 701, 763, 768, 775, 785, 787, 806, 808, 890–891, 923–924, 1006, 1013, 1085–1086, 1088
TOTAL	21247	3302	84%

Python Unit Test Overview

Tests	Skipped	Failures	Errors	Time
4192	239 💤	0 ❌	0 🔥	1m 12s ⏱️

[Copilot]

Pull request overview

This pull request fixes two critical bugs in the HandoffBuilder's handling of Responses API-style clients, ensuring conversation context and session state are correctly managed across agent handoffs. The fixes prevent "No tool output found" API errors and restore complete conversation history to agents after handoffs.

Changes:

• Fixed stale previous_response_id issue by clearing service_session_id after handoffs
• Restored full conversation context by passing _full_conversation to agents instead of partial _cache
• Added comprehensive regression tests with Responses API mock to prevent future regressions

Reviewed changes

Copilot reviewed 2 out of 2 changed files in this pull request and generated no comments.

File	Description
python/packages/orchestrations/tests/test_handoff_responses.py	New test suite with mock Responses API client to verify handoff invariants: session clearing and context preservation
python/packages/orchestrations/agent_framework_orchestrations/_handoff.py	Two-line fix: copy full conversation to cache before agent runs, and clear service_session_id after handoffs

[TaoChenOSU]

Is this like saying each time it will create a new session in the service?

[moonbox3]

I've got these same fixes in #3911, plus others that I found through testing workflows with handoff + AG-UI. We could add the regression tests from yours to 3911.