Gate experimental context by model capability at session startup - #43147

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## Why

Experimental context activation previously checked the provider and account eligibility without checking model support. Child sessions also inherited token-budget activation from their parent, even when starting fresh with a different model.

## What changed

- Add `ModelInfo.supports_experimental_context`, defaulting to `false`, and enable it for the bundled `gpt-6-astra` model. Require this capability when activating experimental context.
- Snapshot configured token-budget preferences before startup activation. Restore them for fresh child sessions before applying their starting model's defaults, while history forks retain their parent's activation.
- Pass unresolved token-budget preferences to child sessions so they can use their own model's prompts.

## Testing

Extend coverage for unsupported models, model-switch guidance under explicit and experimental activation, and child configuration from both active and inactive parents. Verify that omitted capability metadata defaults to `false`.

GitOrigin-RevId: 02df9e171682267232fa923d5ea3f7af36527808