ci: restore Linux remote-env PR tests

[starr-openai]

Summary

• restore a Linux PR-time remote-env lane in rust-ci.yml
• run codex-core under cargo nextest after booting the Docker-backed CODEX_TEST_REMOTE_ENV
• keep the existing fast PR workflow shape while bringing back the remote executor coverage lost when the full Cargo matrix moved to rust-ci-full.yml
• document the restored PR check in .github/workflows/README.md

Why

CODEX_TEST_REMOTE_ENV coverage was introduced in #14869, but the later CI split moved the only Docker setup + remote test invocation out of PR CI and into rust-ci-full.yml on main. That left the remote executor path present in the codebase but absent from pre-merge signal.

This change restores that signal on Linux without bringing back the full old Cargo matrix.

Validation

• parsed .github/workflows/rust-ci.yml as YAML locally
• reviewed the workflow diff against rust-ci-full.yml to keep the Docker setup path aligned
• relying on PR CI for full execution on the runner with Docker

[starr-openai]

Codex babysitter update: the PR branch was rebased onto current main to clear a merge conflict in codex-rs/core/tests/suite/client.rs. Mergeability is restored on the new SHA and CI is rerunning now.