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/plugins/manager_tests.rs

@@ -1,5 +1,4 @@
 use super::*;
-use crate::auth::CodexAuth;
 use crate::config::CONFIG_TOML_FILE;
 use crate::config::ConfigBuilder;
 use crate::config::types::McpServerTransportConfig;
@@ -15,6 +14,7 @@ use crate::plugins::test_support::write_curated_plugin_sha_with as write_curated
 use crate::plugins::test_support::write_file;
 use crate::plugins::test_support::write_openai_curated_marketplace;
 use codex_app_server_protocol::ConfigLayerSource;
+use codex_login::CodexAuth;
 use codex_protocol::protocol::Product;
 use pretty_assertions::assert_eq;
 use std::fs;