Python: Fix the Responses agent msg chaining with reasoning models

[moonbox3]

Motivation and Context

When running a reasoning model with the OpenAI responses agent, it was producing 400s due to the way we were either including or not including FCC related to tool calls. This PR fixes it for both the default (store_enabled=True) and the case where uses don't want to use OpenAI's previous response id as a pseudo-thread (store_enabled=False).

Description

• Closes Python: Bug: AzureResponsesAgent with reasoning model doesn't work #12843

Contribution Checklist

• The code builds clean without any errors or warnings
• The PR follows the SK Contribution Guidelines and the pre-submission formatting script raises no violations
• All unit tests pass, and I have added new tests where possible
• I didn't break anyone 😄

[moonbox3]

Python Test Coverage Report •

File	Stmts	Miss	Cover	Missing
agents/open_ai
responses_agent_thread_actions.py	368	104	71%	169, 186, 199, 210–211, 224, 381–383, 385, 399, 404, 411, 429–430, 434, 446, 480–482, 485, 503–504, 515–517, 521, 525–526, 530–532, 543–545, 567, 569–570, 577–578, 580–581, 583, 585–586, 588–589, 688, 693, 701–702, 704, 710, 715, 720–722, 728–730, 735–736, 738–743, 745, 749–750, 752, 756, 760, 765–766, 771, 774–775, 846–849, 890–891, 895–897, 899, 924–925, 927–931, 933, 943–944, 952, 956, 963, 969, 1033
data
vector.py	656	114	82%	83, 413, 579, 698, 896–899, 905, 907–908, 1026, 1064–1065, 1068, 1075, 1095–1102, 1104, 1106–1107, 1109, 1111, 1114–1119, 1121–1126, 1148, 1171, 1308, 1459, 1474, 1480–1481, 1483, 1510, 1584–1585, 1597–1598, 1627, 1712, 1717–1720, 1834, 1861–1862, 1901, 1921, 1929–1930, 1942, 1949, 1994, 1997, 2051–2053, 2056, 2065, 2088, 2090–2095, 2097–2102, 2106–2112, 2116–2121, 2124–2126, 2128, 2156, 2170, 2178, 2217, 2241, 2255, 2301, 2341
TOTAL	26836	4612	82%

Python Unit Test Overview

Tests	Skipped	Failures	Errors	Time
3681	22 💤	0 ❌	0 🔥	1m 55s ⏱️

[dmytrostruk]

nit: Do we want to add a sample how to use Responses agent with reasoning model?

[moonbox3]

nit: Do we want to add a sample how to use Responses agent with reasoning model?

Good question. A community member is working on adding the reasoning summaries. Once we have those, then yes, we should have a sample that reflects how to configure these summaries, and other reasoning-specific config.

Right now, the Responses agent with a reasoning model isn't much different than a model like gpt-4.1.