.NET: Update compaction docs to show different ways to use a Compaction Strategy with their implications

@westey-m is already working on this.

Since Jul 28, 2026.

Hi!

I'm wondering what the difference is between defining a compaction strategy like this:

```csharp
var compactionStrategy = new ContextWindowCompactionStrategy(
maxContextWindowTokens: 4000,
maxOutputTokens: 800);

var agent = chatClient
.AsAIAgent(new ChatClientAgentOptions
{
ChatOptions = new()
{
Instructions = "You are a helpful assistant.",
},
AIContextProviders = [new CompactionProvider(compactionStrategy)]
});
```

and instead of using it as a `ChatReducer`:

```csharp
var agent = chatClient
.AsAIAgent(new ChatClientAgentOptions
{
ChatOptions = new()
{
Instructions = "You are a helpful assistant.",
},
ChatHistoryProvider = new InMemoryChatHistoryProvider(new()
{
ChatReducer = compactionStrategy.AsChatReducer()
})
});
```

I'm asking because I read the documentation at https://learn.microsoft.com/en-us/agent-framework/agents/conversations/compaction?#registering-through-chatclientagentoptions, but it doesn't mention using the compaction strategy as a ChatReducer.

More generally, what is the recommended way to register a compaction strategy? For example, in Agent Harness I noticed that the strategy is registered both as a `ChatReducer` and via `UseAIContextProviders(...)` on the `ChatClientBuilder`:

https://github.com/microsoft/agent-framework/blob/7b6d2579884b0fde7729342f046ea58847ffdf37/dotnet/src/Microsoft.Agents.AI.Harness/HarnessAgent.cs#L195

https://github.com/microsoft/agent-framework/blob/7b6d2579884b0fde7729342f046ea58847ffdf37/dotnet/src/Microsoft.Agents.AI.Harness/HarnessAgent.cs#L241

Should one of these approaches be preferred, or do they serve different purposes?