[codex] Remove async_trait from first-party code (#27475)

## Why

First-party async traits should expose their `Send` contracts explicitly
without requiring `async_trait`. This completes the migration pattern
established in #27303 and #27304.

## What changed

- Replaced the remaining first-party `async_trait` traits with native
return-position `impl Future + Send` where statically dispatched and
explicit boxed `Send` futures where object safety is required.
- Kept implementations behavior-preserving, outlining existing async
bodies into inherent methods where that keeps the diff reviewable.
- Removed all direct first-party `async-trait` dependencies and the
workspace dependency declaration.
- Added a cargo-deny policy that permits `async-trait` only through the
remaining transitive wrapper crates.
- Updated `rand` from 0.8.5 to 0.8.6 to resolve RUSTSEC-2026-0097 and
keep the full cargo-deny check passing.

## Validation

- `just test -p codex-exec-server`: 216 passed, 2 skipped.
- `just test -p codex-model-provider`: 39 passed.
- `just test -p codex-core` and `just test`: changed tests passed;
remaining failures are environment-sensitive suites unrelated to this
migration.
- `cargo deny check`
- `just fix`
- `just fmt`
- `cargo shear`
- `just bazel-lock-check`

codex-rs/config/src/thread_config/remote.rs

@@ -3,7 +3,6 @@ use std::collections::HashMap;
 use std::num::NonZeroU64;
 use std::time::Duration;
 
-use async_trait::async_trait;
 use codex_model_provider_info::ModelProviderInfo;
 use codex_model_provider_info::WireApi;
 use codex_protocol::config_types::ModelProviderAuthInfo;
@@ -14,6 +13,7 @@ use super::ThreadConfigContext;
 use super::ThreadConfigLoadError;
 use super::ThreadConfigLoadErrorCode;
 use super::ThreadConfigLoader;
+use super::ThreadConfigLoaderFuture;
 use super::ThreadConfigSource;
 use super::UserThreadConfig;
 use proto::thread_config_loader_client::ThreadConfigLoaderClient;
@@ -49,10 +49,7 @@ impl RemoteThreadConfigLoader {
                 )
             })
     }
-}
 
-#[async_trait]
-impl ThreadConfigLoader for RemoteThreadConfigLoader {
     async fn load(
         &self,
         context: ThreadConfigContext,
@@ -73,6 +70,15 @@ impl ThreadConfigLoader for RemoteThreadConfigLoader {
     }
 }
 
+impl ThreadConfigLoader for RemoteThreadConfigLoader {
+    fn load(
+        &self,
+        context: ThreadConfigContext,
+    ) -> ThreadConfigLoaderFuture<'_, Vec<ThreadConfigSource>> {
+        Box::pin(RemoteThreadConfigLoader::load(self, context))
+    }
+}
+
 fn load_thread_config_request(
     context: ThreadConfigContext,
 ) -> tonic::Request<proto::LoadThreadConfigRequest> {
@@ -321,8 +327,7 @@ mod tests {
         expected_cwd: String,
     }
 
-    #[tonic::async_trait]
-    impl thread_config_loader_server::ThreadConfigLoader for TestServer {
+    impl TestServer {
         async fn load(
             &self,
             request: Request<proto::LoadThreadConfigRequest>,
@@ -341,6 +346,26 @@ mod tests {
         }
     }
 
+    impl thread_config_loader_server::ThreadConfigLoader for TestServer {
+        fn load<'a, 'async_trait>(
+            &'a self,
+            request: Request<proto::LoadThreadConfigRequest>,
+        ) -> std::pin::Pin<
+            Box<
+                dyn std::future::Future<
+                        Output = Result<Response<proto::LoadThreadConfigResponse>, Status>,
+                    > + Send
+                    + 'async_trait,
+            >,
+        >
+        where
+            'a: 'async_trait,
+            Self: 'async_trait,
+        {
+            Box::pin(TestServer::load(self, request))
+        }
+    }
+
     #[tokio::test]
     async fn load_thread_config_calls_remote_service() {
         let cwd = workspace_dir().join("project");