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/cli/src/login.rs

@@ -7,14 +7,14 @@
 //! into a one-shot CLI command while still producing a durable `codex-login.log` artifact that
 //! support can request from users.
 
-use codex_core::CodexAuth;
-use codex_core::auth::AuthCredentialsStoreMode;
-use codex_core::auth::AuthMode;
-use codex_core::auth::CLIENT_ID;
-use codex_core::auth::login_with_api_key;
-use codex_core::auth::logout;
 use codex_core::config::Config;
+use codex_login::AuthCredentialsStoreMode;
+use codex_login::AuthMode;
+use codex_login::CLIENT_ID;
+use codex_login::CodexAuth;
 use codex_login::ServerOptions;
+use codex_login::login_with_api_key;
+use codex_login::logout;
 use codex_login::run_device_code_login;
 use codex_login::run_login_server;
 use codex_protocol::config_types::ForcedLoginMethod;

codex-rs/cli/src/wsl_paths.rs

@@ -1,7 +1,7 @@
 use std::ffi::OsStr;
 
 /// Returns true if the current process is running under WSL.
-pub use codex_core::env::is_wsl;
+pub use codex_utils_path::env::is_wsl;
 
 /// Convert a Windows absolute path (`C:\foo\bar` or `C:/foo/bar`) to a WSL mount path (`/mnt/c/foo/bar`).
 /// Returns `None` if the input does not look like a Windows drive path.