[docs] Suggest using dart pub add for adding dependencies

[parlough]

Suggest using dart pub add instead of manually adding various packages so developers don't end up using outdated versions. Also removes some outdated mentions of using a git dependency.

[gemini-code-assist]

Code Review

This pull request updates the documentation to recommend using dart pub add for managing dependencies, which is a great improvement for developer experience. My review focuses on a further refinement: using flutter pub add instead, as it is the idiomatic and recommended command for Flutter projects. This ensures consistency with Flutter's official documentation and helps prevent potential SDK versioning issues. The suggested changes are applied across all updated documentation files for consistency.