docs: Enhance quickstart guide with admonitions and examples

- Convert blockquotes to GFM admonitions for better visibility
- Add current directory initialization example
- Expand process to 6 steps with clarify, analyze, checklist, implement
- Update example with separate clarify commands
- Add proper links in Next Steps

Fixes #906, #472
Generated-by: GitHub Copilot <github.copilot@github.com>

Signed-off-by: Ashley Childress <6563688+anchildress1@users.noreply.github.com>