Python: WIP: Improve Handoff context management

[TaoChenOSU]

Motivation and Context

Addresses #4411

Description

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.

[TaoChenOSU]

This PR is waiting for this issue to be resolved: #4488

[markwallace-microsoft]

Python Test Coverage Report •

File	Stmts	Miss	Cover	Missing
packages/core/agent_framework/_workflows
_agent_executor.py	211	27	87%	97, 113, 168–169, 221–222, 224–225, 255–257, 265–267, 275–277, 279, 283, 287, 291–292, 337, 405–406, 471, 490
_runner.py	173	2	98%	304–305
packages/orchestrations/agent_framework_orchestrations
_handoff.py	337	53	84%	104–105, 107, 162–172, 174, 176, 178, 183, 313, 338, 365, 391, 454–455, 498, 506, 510–511, 549–551, 556–558, 676, 679, 692, 754, 759, 766, 776, 778, 797, 799, 881–882, 914–915, 997, 1004, 1076–1077, 1079
_orchestrator_helpers.py	15	2	86%	73–74
TOTAL	22656	2579	88%

Python Unit Test Overview

Tests	Skipped	Failures	Errors	Time
4955	20 💤	0 ❌	0 🔥	1m 20s ⏱️

[moonbox3]

Superseded by #5136.