Convert existing '## Sample code' samples to '{@tool sample}...{@end-tool}' form. (#24077)

This converts existing ## Sample code samples to {@tool sample}...{@end-tool} form.

Also:
1. Fixed a minor bug in analyze-sample-code.dart
2. Made the snippet tool only insert descriptions if the description is non-empty.
3. Moved the Card diagram to before the code sample.