[codex] Add full Rust PR validation

[romgenie]

Summary

• Adds a dedicated GitHub Actions workflow for full Rust PR validation.
• Includes narrow CI-readiness fixes needed for the new workflow to pass on Windows and Linux.

Context

• Related issue/user request: GitHub-side testing setup for the research fork.
• Scope: .github/workflows/rust-ci.yml plus narrow test/build fixes surfaced by the new CI and local suite.
• Non-goals: Enabling Actions through the GitHub UI, merging PRs, or changing hosted-review behavior.

Changes

• Runs Rust formatting, workspace check, Clippy with warnings denied, and the full workspace test suite on pull requests and manual dispatch.
• Installs the Linux system dependencies required by the workspace build.
• Uses Cargo registry/build caching keyed by src-rust/Cargo.lock.
• Adds test-only home isolation for Windows tests that previously read the real user profile.
• Fixes Linux-only TUI image paste build/Clippy issues surfaced by remote CI.

Validation

Record exact commands and outcomes. Mark items N/A with a reason when they do not apply.

• git diff --check / git show --check - passed.
• cargo fmt --all -- --check - passed locally.
• cargo check --workspace - passed locally.
• cargo clippy --workspace --all-targets -- -D warnings - passed locally.
• cargo test --workspace --quiet - passed locally.
• Targeted/manual checks: PR 6 Rust CI and TUI Tests passed on GitHub Actions.
• Not run: N/A.

PR Readiness

• Diff is limited to the intended CI/testing files and fixes surfaced by CI.
• Generated files were not edited by hand.
• User-facing docs/help were updated or are not needed.
• No secrets, credentials, local paths, or unrelated logs are included.
• Remaining risks or follow-up work are listed above.

Remaining risk: Rust CI is introduced by this PR, so the hosted-review PRs currently receive the pre-existing TUI Tests workflow only until this PR lands on main.