Python: preserve approval context across resume paths

[eavanvalkenburg]

Motivation & Context

Tool approval resume has two context-sensitive gaps. A sessionless Agent.run(...) silently drops a valid approval when any context provider causes the framework to create a fresh per-run session, while AG-UI adapter-local approval execution loses the documented function_invocation_kwargs runtime context before agent.run(...) begins.

This is the upper layer of a dependent PR chain and depends on microsoft#8428.

Description & Review Guide

• What are the major changes? Mark framework-created context-provider sessions with the existing run-local ownership marker so they do not become authoritative approval state; preserve caller-supplied and persistent session authority. Thread function_invocation_kwargs through the programmatic AG-UI entry points, and build adapter-local FunctionInvocationContext.kwargs only from that mapping plus options["additional_function_arguments"], with options taking precedence. Add focused core, AG-UI, and combined context-provider resume regressions.
• What is the impact of these changes? The documented sessionless approval flow now behaves consistently with or without context providers, without weakening fail-closed session-backed binding. Approved AG-UI tools retain runtime identity and policy context without receiving unrelated AG-UI session, tool-list, middleware, or provider-option kwargs.
• What do you want reviewers to focus on? The framework-owned versus caller-owned session boundary, and the AG-UI runtime-kwargs filtering/precedence at adapter-local execution.

Related Issue

Depends on microsoft#8428.

Fixes microsoft#8410

Fixes microsoft#8132

No other open pull request currently references either issue.

Contribution Checklist

• The code builds clean without any errors or warnings
• All unit tests pass, and I have added new tests where possible
• The PR follows the Contribution Guidelines
• This PR is linked to an issue and there is no other open PR for this issue (see Related Issue above).
• This is not a breaking change. If it is a breaking change, add the breaking change label (or add "[BREAKING]" to the title prefix, before or after any language prefix) — a workflow keeps the label and title prefix in sync automatically.

[eavanvalkenburg]

Superseded by microsoft#8433, which targets the upstream repository as requested.