docs: improve install instructions and troubleshooting in README

[ulises-jeremias]

Context

Add yay/paru install commands, version sync note vs PyPI, and link to Discord.

[ulises-jeremias]

Taking this one myself — Homebrew/AUR packaging work needs org-specific permissions (tap publish, AUR credentials, distribution secrets), so it is not a good fit for external contributors right now.

If you want to help with related docs/tests that do not require those secrets, ping me in Discord and we can carve out a safe slice.