Migrate direct HTTP consumers to codex-http-client (#31331)

## Why

#31323 introduces `codex-http-client` and leaves compatibility
re-exports in `codex-client`. Low-level HTTP consumers should depend on
the crate that now owns those APIs rather than continuing through the
transitional compatibility layer.

This stacked follow-up makes that ownership explicit and moves the
repository toward enforcing the abstraction without mixing call-site
churn into the extraction itself.

## What changed

- Switched `codex-backend-client`, `codex-cloud-tasks`,
`codex-exec-server`, `codex-login`, and `codex-model-provider` from
`codex-client` to `codex-http-client` where they only use low-level HTTP
APIs.
- Added the direct dependency to `codex-api` for its custom-CA request
and websocket paths while retaining `codex-client` for higher-level
retry and transport policy.
- Updated imports and normalized login's internal client type name from
`CodexHttpClient` to `HttpClient`, while preserving its existing
`CodexRequestBuilder` re-export.
- Updated `Cargo.lock` to reflect the new direct dependency edges.

## Review guide

This PR is intentionally mechanical: 20 files and 92 changed lines, with
no runtime logic changes. The largest diff is
`codex-rs/login/src/auth/default_client.rs`, where the only
semantic-looking changes are type and import renames. The remaining
source changes replace `codex_client` import paths with
`codex_http_client`; the manifest and lockfile changes mirror those
imports.

## Test plan

- Compile-checked `codex-api`, `codex-backend-client`,
`codex-cloud-tasks`, `codex-exec-server`, `codex-login`, and
`codex-model-provider` together.

codex-rs/backend-client/Cargo.toml

@@ -19,7 +19,7 @@ serde_json = "1"
 reqwest = { version = "0.12", default-features = false, features = ["json", "rustls-tls"] }
 codex-backend-openapi-models = { path = "../codex-backend-openapi-models" }
 codex-api = { workspace = true }
-codex-client = { workspace = true }
+codex-http-client = { workspace = true }
 codex-login = { workspace = true }
 codex-model-provider = { workspace = true }
 codex-protocol = { workspace = true }

codex-rs/backend-client/src/client.rs

@@ -9,8 +9,8 @@ use crate::types::TokenUsageProfile;
 use crate::types::TurnAttemptsSiblingTurnsResponse;
 use anyhow::Result;
 use codex_api::SharedAuthProvider;
-use codex_client::build_reqwest_client_with_custom_ca;
-use codex_client::with_chatgpt_cloudflare_cookie_store;
+use codex_http_client::build_reqwest_client_with_custom_ca;
+use codex_http_client::with_chatgpt_cloudflare_cookie_store;
 use codex_login::CodexAuth;
 use codex_login::default_client::get_codex_user_agent;
 use codex_protocol::account::PlanType as AccountPlanType;