Installation documentation and distribution

[tale]

For new users to adopt rootbeer, there need to be clear installation paths:

• Homebrew tap — create a homebrew-tap repo with a formula
• Cargo install — ensure cargo install rootbeer works cleanly (publish to crates.io or document git install)
• Nix flake — the flake already exists, document how to use it (nix run, nix profile install)
• Pre-built binaries — attach to GitHub releases (pairs with CI release workflow in GitHub Actions CI pipeline #18)
• Getting started updates — the docs getting-started page should cover installation for each method and a quick 2-minute first run

Also update the root README with a concise install section and a quick demo.