## Why
The token budget feature tells the model how much room remains in the
current context window. When the model decides the current window is no
longer useful, it needs a way to ask Codex to start over with a fresh
context window without spending tokens on a compaction summary.
This PR adds that model-requestable escape hatch on top of #27438.
## What changed
- Added a direct-model-only `new_context` tool behind
`Feature::TokenBudget`.
- Stores the tool request on `AutoCompactWindow` and consumes it after
sampling so the next follow-up request in the same turn starts in the
new window.
- Starts the new window as a no-summary compaction checkpoint that
contains only fresh initial context, not preserved conversation history.
- Keeps the new window aligned with token-budget startup context,
including the `Current context window Z` message.
- Added integration coverage and a snapshot showing the same-turn
`new_context` flow into a fresh full-context follow-up request.
## Validation
- `just test -p codex-core token_budget`
pakrym-oai
87ab01834a