core: remove cross-crate re-exports from lib.rs (#16512)

## Why

`codex-core` was re-exporting APIs owned by sibling `codex-*` crates,
which made downstream crates depend on `codex-core` as a proxy module
instead of the actual owner crate.

Removing those forwards makes crate boundaries explicit and lets leaf
crates drop unnecessary `codex-core` dependencies. In this PR, this
reduces the dependency on `codex-core` to `codex-login` in the following
files:

```
codex-rs/backend-client/Cargo.toml
codex-rs/mcp-server/tests/common/Cargo.toml
```

## What

- Remove `codex-rs/core/src/lib.rs` re-exports for symbols owned by
`codex-login`, `codex-mcp`, `codex-rollout`, `codex-analytics`,
`codex-protocol`, `codex-shell-command`, `codex-sandboxing`,
`codex-tools`, and `codex-utils-path`.
- Delete the `default_client` forwarding shim in `codex-rs/core`.
- Update in-crate and downstream callsites to import directly from the
owning `codex-*` crate.
- Add direct Cargo dependencies where callsites now target the owner
crate, and remove `codex-core` from `codex-rs/backend-client`.

codex-rs/core/src/client.rs

@@ -33,7 +33,6 @@ use std::sync::atomic::Ordering;
 use crate::api_bridge::CoreAuthProvider;
 use crate::api_bridge::auth_provider_from_auth;
 use crate::api_bridge::map_api_error;
-use crate::auth::UnauthorizedRecovery;
 use crate::auth_env_telemetry::AuthEnvTelemetry;
 use crate::auth_env_telemetry::collect_auth_env_telemetry;
 use codex_api::CompactClient as ApiCompactClient;
@@ -60,6 +59,12 @@ use codex_api::create_text_param_for_request;
 use codex_api::error::ApiError;
 use codex_api::requests::responses::Compression;
 use codex_api::response_create_client_metadata;
+use codex_login::AuthManager;
+use codex_login::AuthMode;
+use codex_login::CodexAuth;
+use codex_login::RefreshTokenError;
+use codex_login::UnauthorizedRecovery;
+use codex_login::default_client::build_reqwest_client;
 use codex_otel::SessionTelemetry;
 use codex_otel::current_span_w3c_trace_context;
 
@@ -71,6 +76,7 @@ use codex_protocol::models::ResponseItem;
 use codex_protocol::openai_models::ModelInfo;
 use codex_protocol::openai_models::ReasoningEffort as ReasoningEffortConfig;
 use codex_protocol::protocol::SessionSource;
+use codex_protocol::protocol::SubAgentSource;
 use codex_protocol::protocol::W3cTraceContext;
 use codex_tools::create_tools_json_for_responses_api;
 use eventsource_stream::Event;
@@ -91,14 +97,9 @@ use tracing::instrument;
 use tracing::trace;
 use tracing::warn;
 
-use crate::AuthManager;
-use crate::auth::AuthMode;
-use crate::auth::CodexAuth;
-use crate::auth::RefreshTokenError;
 use crate::client_common::Prompt;
 use crate::client_common::ResponseEvent;
 use crate::client_common::ResponseStream;
-use crate::default_client::build_reqwest_client;
 use crate::error::CodexErr;
 use crate::error::Result;
 use crate::flags::CODEX_RS_SSE_FIXTURE;
@@ -460,13 +461,11 @@ impl ModelClient {
         let mut extra_headers = ApiHeaderMap::new();
         if let SessionSource::SubAgent(sub) = &self.state.session_source {
             let subagent = match sub {
-                crate::protocol::SubAgentSource::Review => "review".to_string(),
-                crate::protocol::SubAgentSource::Compact => "compact".to_string(),
-                crate::protocol::SubAgentSource::MemoryConsolidation => {
-                    "memory_consolidation".to_string()
-                }
-                crate::protocol::SubAgentSource::ThreadSpawn { .. } => "collab_spawn".to_string(),
-                crate::protocol::SubAgentSource::Other(label) => label.clone(),
+                SubAgentSource::Review => "review".to_string(),
+                SubAgentSource::Compact => "compact".to_string(),
+                SubAgentSource::MemoryConsolidation => "memory_consolidation".to_string(),
+                SubAgentSource::ThreadSpawn { .. } => "collab_spawn".to_string(),
+                SubAgentSource::Other(label) => label.clone(),
             };
             if let Ok(val) = HeaderValue::from_str(&subagent) {
                 extra_headers.insert("x-openai-subagent", val);
@@ -574,7 +573,7 @@ impl ModelClient {
             websocket_connect_timeout,
             ApiWebSocketResponsesClient::new(api_provider, api_auth).connect(
                 headers,
-                crate::default_client::default_headers(),
+                codex_login::default_client::default_headers(),
                 turn_state,
                 Some(websocket_telemetry),
             ),
@@ -972,7 +971,7 @@ impl ModelClientSession {
             ))
     }
 
-    fn responses_request_compression(&self, auth: Option<&crate::auth::CodexAuth>) -> Compression {
+    fn responses_request_compression(&self, auth: Option<&CodexAuth>) -> Compression {
         if self.client.state.enable_request_compression
             && auth.is_some_and(CodexAuth::is_chatgpt_auth)
             && self.client.state.provider.is_openai()
@@ -1025,7 +1024,7 @@ impl ModelClientSession {
         let auth_manager = self.client.state.auth_manager.clone();
         let mut auth_recovery = auth_manager
             .as_ref()
-            .map(super::auth::AuthManager::unauthorized_recovery);
+            .map(AuthManager::unauthorized_recovery);
         let mut pending_retry = PendingUnauthorizedRetry::default();
         loop {
             let client_setup = self.client.current_client_setup().await?;
@@ -1114,7 +1113,7 @@ impl ModelClientSession {
 
         let mut auth_recovery = auth_manager
             .as_ref()
-            .map(super::auth::AuthManager::unauthorized_recovery);
+            .map(AuthManager::unauthorized_recovery);
         let mut pending_retry = PendingUnauthorizedRetry::default();
         loop {
             let client_setup = self.client.current_client_setup().await?;