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/test_support.rs

@@ -14,8 +14,6 @@ use codex_protocol::openai_models::ModelPreset;
 use codex_protocol::openai_models::ModelsResponse;
 use once_cell::sync::Lazy;
 
-use crate::AuthManager;
-use crate::CodexAuth;
 use crate::ModelProviderInfo;
 use crate::ThreadManager;
 use crate::config::Config;
@@ -23,6 +21,8 @@ use crate::models_manager::collaboration_mode_presets;
 use crate::models_manager::manager::ModelsManager;
 use crate::thread_manager;
 use crate::unified_exec;
+use codex_login::AuthManager;
+use codex_login::CodexAuth;
 
 static TEST_MODEL_PRESETS: Lazy<Vec<ModelPreset>> = Lazy::new(|| {
     let file_contents = include_str!("../models.json");