Context-size configuration is lost for extension-provided models in Agent Host

Hi! I’m working on a `LanguageModelChatProvider` for Vercel AI Gateway, and I ran into what looks like an Agent Host projection gap.

I first noticed this through the product: the Vercel models work in both normal Chat and a Local Agent Host session, but the Context Size dropdown only appears in normal Chat.

The provider already includes `contextSize` choices in the model's `configurationSchema`. Normal Chat renders those choices and passes the selection back to the provider. When the same model is used through Agent Host, the model still appears and works, but that configuration is no longer available.

## Reproduction

1. Install an extension that contributes a language model with `configurationSchema.properties.contextSize`.
2. Select the model in normal Chat and confirm that Context Size is available.
3. Start a Local session from the Agents view.
4. Select the same model and open its configuration.

The Context Size control is missing in the Agent Host session.

I think this is adjacent to #328336 and #320824. #329892 is also close, although I’m not sure it’s exactly the same question: that issue is about declaring context-size choices in `chatLanguageModels.json`, while in this case the extension provider has already declared them and normal Chat can render them.

Looking through the current path, it seems like Agent Host reconstructs the reasoning-effort configuration explicitly, but doesn't carry the provider's context-size choices—or its configuration schema more generally. I may be missing a supported hook here.

What is the intended boundary? Should Agent Host preserve the model configuration supplied by an extension provider, or should context size become another explicit capability carried through the bridge?

If there’s already a supported way for a provider extension to make this configuration available in Agent Host, I’d be happy to use it.