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/tools/spec.rs

@@ -1,4 +1,3 @@
-use crate::mcp_connection_manager::ToolInfo;
 use crate::shell::Shell;
 use crate::shell::ShellType;
 use crate::tools::code_mode::PUBLIC_TOOL_NAME;
@@ -10,6 +9,7 @@ use crate::tools::handlers::multi_agents_common::MIN_WAIT_TIMEOUT_MS;
 use crate::tools::registry::ToolRegistryBuilder;
 use crate::tools::registry::tool_handler_key;
 use codex_mcp::mcp::CODEX_APPS_MCP_SERVER_NAME;
+use codex_mcp::mcp_connection_manager::ToolInfo;
 use codex_protocol::dynamic_tools::DynamicToolSpec;
 use codex_protocol::openai_models::ApplyPatchToolType;
 use codex_protocol::openai_models::ConfigShellToolType;