[apps] Store apps tool cache in disk to reduce startup time. (#11822)

We now write MCP tools from installed apps to disk cache so that they
can be picked up instantly at startup. We still do a fresh fetch from
remote MCP server but it's non blocking unless there's a cache miss.

- [x] Store apps tool cache in disk to reduce startup time.

codex-rs/core/src/codex.rs

@@ -149,6 +149,7 @@ use crate::mcp::effective_mcp_servers;
 use crate::mcp::maybe_prompt_and_install_mcp_dependencies;
 use crate::mcp::with_codex_apps_mcp;
 use crate::mcp_connection_manager::McpConnectionManager;
+use crate::mcp_connection_manager::codex_apps_tools_cache_key;
 use crate::mcp_connection_manager::filter_codex_apps_mcp_tools_only;
 use crate::mcp_connection_manager::filter_mcp_tools_by_name;
 use crate::mcp_connection_manager::filter_non_codex_apps_mcp_tools_only;
@@ -1420,6 +1421,8 @@ impl Session {
             &session_configuration.approval_policy,
             tx_event.clone(),
             sandbox_state,
+            config.codex_home.clone(),
+            codex_apps_tools_cache_key(auth),
         )
         .await;
         {
@@ -3068,6 +3071,8 @@ impl Session {
             &turn_context.config.permissions.approval_policy,
             self.get_tx_event(),
             sandbox_state,
+            config.codex_home.clone(),
+            codex_apps_tools_cache_key(auth.as_ref()),
         )
         .await;
         {