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/model-provider/src/amazon_bedrock/auth.rs

@@ -6,9 +6,9 @@ use codex_api::SharedAuthProvider;
 use codex_aws_auth::AwsAuthContext;
 use codex_aws_auth::AwsAuthError;
 use codex_aws_auth::AwsRequestToSign;
-use codex_client::Request;
-use codex_client::RequestBody;
-use codex_client::RequestCompression;
+use codex_http_client::Request;
+use codex_http_client::RequestBody;
+use codex_http_client::RequestCompression;
 use codex_login::auth::BedrockApiKeyAuth;
 use codex_model_provider_info::ModelProviderAwsAuthInfo;
 use codex_protocol::error::CodexErr;