.NET: run-scoped context with lifecycle hooks for agent decorators

@westey-m is already working on this.

Since Aug 18, 2026.

## Problem

The framework has no run-scoped context object with lifecycle attach points that an extension can use to carry per-run state and act at well-defined moments of a `ChatClientAgent` run. `AIAgent.CurrentRunContext` is a read-only info object, and there is no hook between "the run's final response exists" and "providers are notified / the response is returned".

The agent-hooks integration (#7564) mimics a run scope with an `AsyncLocal` set by its outermost decorator, which works but produces one genuinely awkward mechanism: end-of-run persistence notifications capture the **inner agent's own message list**, assembled before any outer decorator ran. For a streamed run whose output the enforcement transforms after buffering, the deferred persistence would therefore write pre-transform content — so the gating providers substitute the verdicted messages at flush time via state smuggled through the AsyncLocal (`AgentHooksRunState.VerdictedResponseMessages`, consumed in `AgentHooksGatingChatHistoryProvider`/`AgentHooksGatingAIContextProvider`). It is correct and regression-tested, but it is exactly the kind of coupling a framework-owned run context would eliminate.

## Proposed shape (for discussion)

A framework-owned run scope with lifecycle attach points, e.g.:

- run-start / run-end callbacks with access to a mutable per-run property bag;
- a "response finalized, providers not yet notified" hook where a decorator can observe/replace the response messages that will be persisted (which would make deferral-and-substitution unnecessary: the notification would simply be built after outer decorators finish);
- flowing the scope across the streaming drain the same way `AIAgent.RunStreamingAsync` already re-establishes `CurrentRunContext` after each yield.

## Context

- PR #7564 (concrete mechanism: `AgentHooksRunState` (AsyncLocal), `VerdictedResponseMessages` substitution in the gating providers, `RunPersistenceGate` flush ordering in `AgentHooksAgent`)
- Review thread: https://github.com/microsoft/agent-framework/pull/7564#discussion_r3804862167
- Related: companion issues #7726 (addressable pipeline positions) and #7728 (interceptable providers) and #7718

Not urgent (per the review thread). cc @westey-m