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/exec/src/lib.rs

@@ -51,8 +51,6 @@ use codex_arg0::Arg0DispatchPaths;
 use codex_cloud_requirements::cloud_requirements_loader_for_storage;
 use codex_core::LMSTUDIO_OSS_PROVIDER_ID;
 use codex_core::OLLAMA_OSS_PROVIDER_ID;
-use codex_core::auth::AuthConfig;
-use codex_core::auth::enforce_login_restrictions;
 use codex_core::check_execpolicy_for_warnings;
 use codex_core::config::Config;
 use codex_core::config::ConfigBuilder;
@@ -67,6 +65,10 @@ use codex_core::format_exec_policy_error_with_source;
 use codex_core::path_utils;
 use codex_feedback::CodexFeedback;
 use codex_git_utils::get_git_repo_root;
+use codex_login::AuthConfig;
+use codex_login::default_client::set_default_client_residency_requirement;
+use codex_login::default_client::set_default_originator;
+use codex_login::enforce_login_restrictions;
 use codex_otel::set_parent_from_context;
 use codex_otel::traceparent_context_from_env;
 use codex_protocol::config_types::SandboxMode;
@@ -105,8 +107,6 @@ use uuid::Uuid;
 use crate::cli::Command as ExecCommand;
 use crate::event_processor::CodexStatus;
 use crate::event_processor::EventProcessor;
-use codex_core::default_client::set_default_client_residency_requirement;
-use codex_core::default_client::set_default_originator;
 
 const DEFAULT_ANALYTICS_ENABLED: bool = true;