docs: add mdBook user guide and Pages publishing

[shinaoka]

Summary

• add an mdBook-based Rust user guide covering the same topics as the Julia guide
• validate guide examples through compiled source files and add docs checks to CI
• publish the user guide to GitHub Pages and finalize crate dual-licensing metadata

Test Plan

• cargo fmt --all -- --check
• cargo clippy --all-targets -- -D warnings
• cargo nextest run --release
• cargo test --doc
• ./scripts/test-book-examples.sh
• mdbook build