## Why
Prototype whether the harness can invoke the `mcp_history` MCP while
constructing full initial context and expose its thread hint to the
model without requiring a model-issued tool call.
The prototype builds on the context-window lineage added by #29256 and
is now based directly on `main`.
## What changed
- Call `mcp_history/thread_hint` with no arguments while building the
full `<token_budget>` context.
- Pass the current `threadId` through MCP request metadata, matching the
normal MCP tool-call path.
- Serialize only the unstructured `content` result and append it inside
`<token_budget>` when the call succeeds.
- Omit the additional context when the MCP call or content serialization
fails.
## Prototype limitations
- The direct call bypasses the normal model-initiated MCP approval,
lifecycle-event, telemetry, and result-sanitization path.
- The call has no prototype-specific timeout, result-size cap, or
per-window cache.
- MCP latency is added to full-context construction, including
applicable compaction paths.
## Validation
- `just test -p codex-core token_budget`
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