Abstracting async hooks out from components
The general approach looks just fine. The logic behind data retrieval isn't entirely related to the rendering of components, so putting it into a custom hook instead makes good sense, especially if other components might need the data as well.
A few suggestions:

React recommends that the function names of custom hooks start with use, to clearly indicate that it's a hook and that other hooks (like useEffect) can be used inside it.
If other components might need to use the summaries as well, or if this component may get completely unmounted and then re-mounted again, consider whether you can use the summaries that were retrieved previously instead of fetching them again. (Or maybe you do want to fetch them again regardless - think about what you want.)
There doesn't really appear to be error handling, other than setSummaries([]). It would be more user friendly to indicate to the user if there's an error (and, at least in the development environment, to log the error).
Having both a ContentListContainer and a ContentList seems odd, since ContentListContainer is empty except for the custom hook call. If you aren't planning to add more stuff to the container, consider removing ContentListContainer entirely and putting the hook call into ContentList instead.