What is the problem? Please describe.
The CatalogSearchIterator only provides a subset of attributes returned by the API as direct attributes, namely timestamp, geometry and id. But the API provides more information such as e.g. cloud cover and cannot be access directly through the package.
Here's the solution
Provide methods for other attributes returned through the API. The best solution might in fact be to return a GeoPandas GeoDataFrame which should be a well known concept among users (with the drawback of another, big-ish dependency).
Alternatives
The current workaround is to use the (hidden) attribute _fetch_features that will provide the raw GeoJson that can then be parsed manually.
Additional Context
This issue was spawned from this community question.