fix: remove dev-only PostHog skill, add PH + Context7 badges

- Untrack .claude/skills/posthog-integration-javascript_node/ (dev-only)
- Add .claude/skills/ to .gitignore
- Add Product Hunt and Context7 badges to README
- Add Product Hunt embed to docs footer

Co-Authored-By: Glinr <bot@glincker.com>

Author: thegdsks