Add launch-at-login feature card and GitHub star button to homepage

[fredrivett]

Brings the homepage feature list to parity with the README by adding a "Launch at login" feature card, which was the only shipped feature previously missing from the site. Adds a GitHub star button to the hero CTA row, between "View on GitHub" and "Download DMG".

The star button shows a live star count fetched from the GitHub API, displayed as "count ★", and falls back to a bare star icon if the count can't be loaded (e.g. API rate-limited or offline).

🤖 Generated with Claude Code

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Summary by cubic

Adds a “Launch at login” feature card and a GitHub star button with live star count to the homepage hero, bringing the site to parity with the README and adding lightweight social proof.

• New Features
  • Added “Launch at login” feature card.
  • Inserted a GitHub star button between “View on GitHub” and “Download DMG”.
  • Star count fetched from the GitHub API; falls back to a star icon on failure and uses tabular numerals for aligned digits.

^{Written for commit 3d4079c. Summary will update on new commits.}