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/codex_thread.rs

@@ -5,9 +5,6 @@ use crate::config::ConstraintResult;
 use crate::error::CodexErr;
 use crate::error::Result as CodexResult;
 use crate::file_watcher::WatchRegistration;
-use crate::protocol::Event;
-use crate::protocol::Op;
-use crate::protocol::Submission;
 use codex_features::Feature;
 use codex_protocol::config_types::ApprovalsReviewer;
 use codex_protocol::config_types::Personality;
@@ -17,8 +14,11 @@ use codex_protocol::models::ResponseInputItem;
 use codex_protocol::models::ResponseItem;
 use codex_protocol::openai_models::ReasoningEffort;
 use codex_protocol::protocol::AskForApproval;
+use codex_protocol::protocol::Event;
+use codex_protocol::protocol::Op;
 use codex_protocol::protocol::SandboxPolicy;
 use codex_protocol::protocol::SessionSource;
+use codex_protocol::protocol::Submission;
 use codex_protocol::protocol::TokenUsage;
 use codex_protocol::protocol::W3cTraceContext;
 use codex_protocol::user_input::UserInput;
@@ -26,7 +26,7 @@ use std::path::PathBuf;
 use tokio::sync::Mutex;
 use tokio::sync::watch;
 
-use crate::state_db::StateDbHandle;
+use codex_rollout::state_db::StateDbHandle;
 
 #[derive(Clone, Debug)]
 pub struct ThreadConfigSnapshot {