docs: use <picture> with prefers-color-scheme for sponsor and screenshot images

Replace the GitHub-only #gh-*-mode-only fragment hack with standard
<picture> + prefers-color-scheme so light/dark images render correctly
across GitHub, npm, and other markdown renderers. Also add dark-mode
variants to the package README sponsors and drop the ?v= cache-busting
query params.

Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>