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/tui/src/onboarding/auth.rs

@@ -8,9 +8,9 @@ use codex_app_server_protocol::CancelLoginAccountParams;
 use codex_app_server_protocol::ClientRequest;
 use codex_app_server_protocol::LoginAccountParams;
 use codex_app_server_protocol::LoginAccountResponse;
-use codex_core::auth::AuthCredentialsStoreMode;
-use codex_core::auth::read_openai_api_key_from_env;
+use codex_login::AuthCredentialsStoreMode;
 use codex_login::DeviceCode;
+use codex_login::read_openai_api_key_from_env;
 use crossterm::event::KeyCode;
 use crossterm::event::KeyEvent;
 use crossterm::event::KeyEventKind;

codex-rs/tui/src/onboarding/auth/headless_chatgpt_login.rs

@@ -3,7 +3,7 @@
 use codex_app_server_protocol::ClientRequest;
 use codex_app_server_protocol::LoginAccountParams;
 use codex_app_server_protocol::LoginAccountResponse;
-use codex_core::auth::CLIENT_ID;
+use codex_login::CLIENT_ID;
 use codex_login::ServerOptions;
 use codex_login::complete_device_code_login;
 use codex_login::request_device_code;