Token-budget initial context carries thread and context-window lineage that the model should treat as one structured context-window block. Wrapping it in `<context_window>` makes that boundary explicit while preserving the existing window id content.
This adds shared `CONTEXT_WINDOW_*_TAG` protocol constants, updates `TokenBudgetContext` to render with those markers, treats the new wrapper as contextual developer content when mapping history, and refreshes the token-budget request-shape assertions and snapshot.
Verification:
- `just test -p codex-core token_budget`
- `just test -p codex-core recognizes_context_window_as_contextual_developer_content`