docs(public-docs): remove rust install script examples

[kdy1]

Summary

• remove repo-local install script examples from the public-docs pages for cargo-mono, nodeup, and with-watch
• keep public guidance focused on Homebrew, cargo-binstall, and cargo install where applicable
• update public-docs and crate foundation contracts so installer scripts can remain supported without being surfaced in public-docs

Testing

• pnpm --filter public-docs test
• rg -n "scripts/install/cargo-mono|scripts/install/nodeup|scripts/install/with-watch" apps/public-docs
• rg -n "cargo binstall cargo-mono|cargo binstall nodeup|cargo binstall with-watch|cargo install with-watch" apps/public-docs