Start cached MCP servers lazily for subagents (#37261)

## Why

Subagents can reuse cached MCP tool definitions without starting every optional
server before any of its tools are used.

## What changed

- Defer startup for subagent-owned, optional MCP servers when their cache has at
  least one visible, allowed tool, and trigger startup on the first operation
  that needs the live client.
- Keep root sessions, required servers, selected plugin servers, and explicit
  reconnects eager.
- Exclude empty catalogs from cache eligibility and keep dormant servers out of
  the initial startup summary.

## Testing

- Extend MCP tool-cache coverage for eager root startup, unused and filtered
  subagent servers, deferred startup status events, and startup that survives an
  interrupted first tool call.

GitOrigin-RevId: e7528ff08312583a6747cbc6550ea5b6eabda9a6

codex-rs/codex-mcp/src/tool_catalog_cache.rs

@@ -107,7 +107,7 @@ impl Default for ToolCatalogCacheEntry {
 
 impl McpToolCatalogCacheContext {
     pub(crate) fn has_tools(&self) -> bool {
-        self.current_tools().is_some()
+        self.current_tools().is_some_and(|tools| !tools.is_empty())
     }
 
     pub(crate) fn optional_startup_deadline(&self, default_deadline: Instant) -> Instant {