Reuse MCP handlers across sampling steps (#37273)

## Why

MCP tool handlers and their Code Mode definitions are immutable for the lifetime
of a stable MCP binding, so rebuilding them for every sampling step repeats schema
construction unnecessarily.

## What changed

- Cache MCP handlers per session and reuse them while the same binding remains
  active, invalidating the cache when the binding changes.
- Lazily cache schema-free Code Mode definitions on MCP handlers while continuing
  to rebuild definitions for step-local tools whose specifications may change.
- Reapply current app enablement, tool policy, exposure, and plugin schema budgets
  whenever cached handlers are registered for a step.

## Testing

- Cover handler and Code Mode definition reuse, binding invalidation, changing app
  policy, stable continuation schemas, and step-local custom tool updates.

GitOrigin-RevId: 69c5011fb97c08580ac476e7fb2286b1e92e0359

codex-rs/core/src/session/session.rs

@@ -1115,6 +1115,7 @@ impl Session {
                 // Start with an empty connection set. The initialized set is
                 // published after SessionConfigured so MCP events follow it.
                 mcp_runtime,
+                mcp_handler_cache: Default::default(),
                 unified_exec_manager: UnifiedExecProcessManager::new(
                     config.background_terminal_max_timeout,
                 ),