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/state/session_tests.rs

@@ -1,6 +1,7 @@
 use super::*;
 use crate::codex::make_session_configuration_for_tests;
-use crate::protocol::RateLimitWindow;
+use codex_protocol::protocol::CreditsSnapshot;
+use codex_protocol::protocol::RateLimitWindow;
 use pretty_assertions::assert_eq;
 
 #[tokio::test]
@@ -112,7 +113,7 @@ async fn set_rate_limits_carries_credits_and_plan_type_from_codex_to_codex_other
             resets_at: Some(100),
         }),
         secondary: None,
-        credits: Some(crate::protocol::CreditsSnapshot {
+        credits: Some(CreditsSnapshot {
             has_credits: true,
             unlimited: false,
             balance: Some("50".to_string()),
@@ -144,7 +145,7 @@ async fn set_rate_limits_carries_credits_and_plan_type_from_codex_to_codex_other
                 resets_at: Some(200),
             }),
             secondary: None,
-            credits: Some(crate::protocol::CreditsSnapshot {
+            credits: Some(CreditsSnapshot {
                 has_credits: true,
                 unlimited: false,
                 balance: Some("50".to_string()),