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/tasks/mod.rs

@@ -19,7 +19,6 @@ use tracing::info_span;
 use tracing::trace;
 use tracing::warn;
 
-use crate::AuthManager;
 use crate::codex::Session;
 use crate::codex::TurnContext;
 use crate::contextual_user_message::TURN_ABORTED_CLOSE_TAG;
@@ -29,13 +28,10 @@ use crate::hook_runtime::inspect_pending_input;
 use crate::hook_runtime::record_additional_contexts;
 use crate::hook_runtime::record_pending_input;
 use crate::models_manager::manager::ModelsManager;
-use crate::protocol::EventMsg;
-use crate::protocol::TurnAbortReason;
-use crate::protocol::TurnAbortedEvent;
-use crate::protocol::TurnCompleteEvent;
 use crate::state::ActiveTurn;
 use crate::state::RunningTask;
 use crate::state::TaskKind;
+use codex_login::AuthManager;
 use codex_otel::SessionTelemetry;
 use codex_otel::metrics::names::TURN_E2E_DURATION_METRIC;
 use codex_otel::metrics::names::TURN_NETWORK_PROXY_METRIC;
@@ -44,7 +40,12 @@ use codex_otel::metrics::names::TURN_TOOL_CALL_METRIC;
 use codex_protocol::models::ContentItem;
 use codex_protocol::models::ResponseInputItem;
 use codex_protocol::models::ResponseItem;
+use codex_protocol::protocol::EventMsg;
 use codex_protocol::protocol::RolloutItem;
+use codex_protocol::protocol::TokenUsage;
+use codex_protocol::protocol::TurnAbortReason;
+use codex_protocol::protocol::TurnAbortedEvent;
+use codex_protocol::protocol::TurnCompleteEvent;
 use codex_protocol::user_input::UserInput;
 
 use codex_features::Feature;
@@ -405,7 +406,7 @@ impl Session {
                 &[tmp_mem],
             );
             let total_token_usage = self.total_token_usage().await.unwrap_or_default();
-            let turn_token_usage = crate::protocol::TokenUsage {
+            let turn_token_usage = TokenUsage {
                 input_tokens: (total_token_usage.input_tokens
                     - token_usage_at_turn_start.input_tokens)
                     .max(0),