Improve logo transparency for dark theme support

- Remove baked-in checkerboard background using flood-fill from corners
- Apply fuzz-based transparent white to fix enclosed areas in letter
  counters (P, A, e, a characters)
- Trim excess transparent padding
- Remove duplicate logo from docs/index.rst (html_logo handles sidebar)

Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>

Author: laughingman7743