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/thread_manager.rs

@@ -1,5 +1,3 @@
-use crate::AuthManager;
-use crate::CodexAuth;
 use crate::ModelProviderInfo;
 use crate::OPENAI_PROVIDER_ID;
 use crate::SkillsManager;
@@ -17,9 +15,6 @@ use crate::mcp::McpManager;
 use crate::models_manager::collaboration_mode_presets::CollaborationModesConfig;
 use crate::models_manager::manager::ModelsManager;
 use crate::plugins::PluginsManager;
-use crate::protocol::Event;
-use crate::protocol::EventMsg;
-use crate::protocol::SessionConfiguredEvent;
 use crate::rollout::RolloutRecorder;
 use crate::rollout::truncation;
 use crate::shell_snapshot::ShellSnapshot;
@@ -29,15 +24,20 @@ use crate::tasks::interrupted_turn_history_marker;
 use codex_app_server_protocol::ThreadHistoryBuilder;
 use codex_app_server_protocol::TurnStatus;
 use codex_exec_server::EnvironmentManager;
+use codex_login::AuthManager;
+use codex_login::CodexAuth;
 use codex_protocol::ThreadId;
 use codex_protocol::config_types::CollaborationModeMask;
 #[cfg(test)]
 use codex_protocol::models::ResponseItem;
 use codex_protocol::openai_models::ModelPreset;
+use codex_protocol::protocol::Event;
+use codex_protocol::protocol::EventMsg;
 use codex_protocol::protocol::InitialHistory;
 use codex_protocol::protocol::McpServerRefreshConfig;
 use codex_protocol::protocol::Op;
 use codex_protocol::protocol::RolloutItem;
+use codex_protocol::protocol::SessionConfiguredEvent;
 use codex_protocol::protocol::SessionSource;
 use codex_protocol::protocol::TurnAbortReason;
 use codex_protocol::protocol::TurnAbortedEvent;