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/arc_monitor.rs

@@ -8,8 +8,9 @@ use tracing::warn;
 use crate::codex::Session;
 use crate::codex::TurnContext;
 use crate::compact::content_items_to_text;
-use crate::default_client::build_reqwest_client;
 use crate::event_mapping::is_contextual_user_message_content;
+use codex_login::CodexAuth;
+use codex_login::default_client::build_reqwest_client;
 use codex_protocol::models::MessagePhase;
 use codex_protocol::models::ResponseItem;
 
@@ -147,10 +148,7 @@ pub(crate) async fn monitor_action(
         .timeout(ARC_MONITOR_TIMEOUT)
         .json(&body)
         .bearer_auth(token);
-    if let Some(account_id) = auth
-        .as_ref()
-        .and_then(crate::auth::CodexAuth::get_account_id)
-    {
+    if let Some(account_id) = auth.as_ref().and_then(CodexAuth::get_account_id) {
         request = request.header("chatgpt-account-id", account_id);
     }