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/tests/suite/personality.rs

@@ -684,7 +684,7 @@ async fn remote_model_friendly_personality_instructions_with_feature() -> anyhow
     let resp_mock = mount_sse_once(&server, sse_completed("resp-1")).await;
 
     let mut builder = test_codex()
-        .with_auth(codex_core::CodexAuth::create_dummy_chatgpt_auth_for_testing())
+        .with_auth(codex_login::CodexAuth::create_dummy_chatgpt_auth_for_testing())
         .with_config(|config| {
             config
                 .features
@@ -804,7 +804,7 @@ async fn user_turn_personality_remote_model_template_includes_update_message() -
     .await;
 
     let mut builder = test_codex()
-        .with_auth(codex_core::CodexAuth::create_dummy_chatgpt_auth_for_testing())
+        .with_auth(codex_login::CodexAuth::create_dummy_chatgpt_auth_for_testing())
         .with_config(|config| {
             config
                 .features