[codex] Remove async_trait from ToolExecutor (#27304)

## Why

We're now [discouraging use of
`async_trait`](https://github.com/openai/codex/pull/20242).

Removing use of `async_trait` from `ToolExecutor` yields a `codex_core`
debug test build speedup of ~78% (from 227.5s to 50.3s) on my machine.

Stacked on #27299, this PR applies the trait change after the handler
bodies have been outlined.

## What

Changed `ToolExecutor::handle` to return an explicit boxed
`ToolExecutorFuture` instead of using `async_trait`.

Updated ToolExecutor implementors to return `Box::pin(...)`, reexported
the future alias through `codex-tools` and `codex-extension-api`, and
removed `codex-tools` direct `async-trait` dependency.

codex-rs/ext/memories/src/tools/ad_hoc_note.rs

@@ -41,7 +41,6 @@ pub(super) struct AddAdHocNoteTool<B> {
     pub(super) metrics_client: Option<MetricsClient>,
 }
 
-#[async_trait::async_trait]
 impl<B> ToolExecutor<ToolCall> for AddAdHocNoteTool<B>
 where
     B: MemoriesBackend,
@@ -57,12 +56,8 @@ where
         )
     }
 
-    async fn handle(
-        &self,
-        call: ToolCall,
-    ) -> Result<Box<dyn codex_extension_api::ToolOutput>, codex_extension_api::FunctionCallError>
-    {
-        self.handle_call(call).await
+    fn handle(&self, call: ToolCall) -> codex_extension_api::ToolExecutorFuture<'_> {
+        Box::pin(self.handle_call(call))
     }
 }
 

codex-rs/ext/memories/src/tools/list.rs

@@ -39,7 +39,6 @@ pub(super) struct ListTool<B> {
     pub(super) metrics_client: Option<MetricsClient>,
 }
 
-#[async_trait::async_trait]
 impl<B> ToolExecutor<ToolCall> for ListTool<B>
 where
     B: MemoriesBackend,
@@ -55,12 +54,8 @@ where
         )
     }
 
-    async fn handle(
-        &self,
-        call: ToolCall,
-    ) -> Result<Box<dyn codex_extension_api::ToolOutput>, codex_extension_api::FunctionCallError>
-    {
-        self.handle_call(call).await
+    fn handle(&self, call: ToolCall) -> codex_extension_api::ToolExecutorFuture<'_> {
+        Box::pin(self.handle_call(call))
     }
 }
 

codex-rs/ext/memories/src/tools/read.rs

@@ -38,7 +38,6 @@ pub(super) struct ReadTool<B> {
     pub(super) metrics_client: Option<MetricsClient>,
 }
 
-#[async_trait::async_trait]
 impl<B> ToolExecutor<ToolCall> for ReadTool<B>
 where
     B: MemoriesBackend,
@@ -54,12 +53,8 @@ where
         )
     }
 
-    async fn handle(
-        &self,
-        call: ToolCall,
-    ) -> Result<Box<dyn codex_extension_api::ToolOutput>, codex_extension_api::FunctionCallError>
-    {
-        self.handle_call(call).await
+    fn handle(&self, call: ToolCall) -> codex_extension_api::ToolExecutorFuture<'_> {
+        Box::pin(self.handle_call(call))
     }
 }
 

codex-rs/ext/memories/src/tools/search.rs

@@ -47,7 +47,6 @@ pub(super) struct SearchTool<B> {
     pub(super) metrics_client: Option<MetricsClient>,
 }
 
-#[async_trait::async_trait]
 impl<B> ToolExecutor<ToolCall> for SearchTool<B>
 where
     B: MemoriesBackend,
@@ -63,12 +62,8 @@ where
         )
     }
 
-    async fn handle(
-        &self,
-        call: ToolCall,
-    ) -> Result<Box<dyn codex_extension_api::ToolOutput>, codex_extension_api::FunctionCallError>
-    {
-        self.handle_call(call).await
+    fn handle(&self, call: ToolCall) -> codex_extension_api::ToolExecutorFuture<'_> {
+        Box::pin(self.handle_call(call))
     }
 }