Context

netclaw-dev/netclaw#1687 changes the native installers to manage PATH automatically and adds an explicit opt-out:

• Unix writes shell-specific startup integration for Bash, zsh, and fish; --skip-shell disables it.
• Windows adds the install directory to the User PATH; -SkipShell disables it.
• A piped Unix installer cannot mutate the parent shell's current PATH, so users must open a new shell or source ~/.netclaw/env before immediately running netclaw.
• Windows users must restart their terminal before a new process inherits the updated User PATH.

The main repository README is updated in #1687, but the website installation and quickstart flow need to be synchronized. Publish the website change with or after the first Netclaw release containing #1687 so the documentation does not get ahead of the released installer scripts.

Required updates

• Update src/content/docs/getting-started/installation.md to describe automatic Unix shell integration and Windows User PATH mutation.
• Document --skip-shell and -SkipShell, including the manual follow-up behavior.
• Explain the current-terminal boundary:
  • Unix: open a new shell or run . ~/.netclaw/env.
  • Windows: restart the terminal.
• Update src/content/docs/getting-started/quickstart.md so the install-to-netclaw init sequence works in practice rather than assuming the current shell was mutated.
• Update the homepage install-to-init presentation and install notes with the same terminal-refresh expectation.
• Correct the homepage macOS claim that Intel Macs are supported; the current installer supports Apple Silicon only.
• Link to feat(install): automate shell PATH integration netclaw#1687 as the behavior source.

Acceptance criteria

• A user following the Linux/macOS quickstart in one terminal is told exactly how to make netclaw resolvable before running netclaw init.
• A Windows user is told that Netclaw is added to User PATH and that the terminal must be restarted.
• Opt-out commands are documented for both installer variants.
• Website architecture claims match the installer-supported macOS targets.