You suggest that the continuation token, is basically an encoding of the query parameters, to fetch results from the API. If you go with this approach, then you don't have to store any state on the server. This is a good approach, because it's simple, but it doesn't solve the issue, where the response from the API changes while you making the paging API calls. The example used in the article is where an order was deleted, while you were calling the API.
I was thinking of using a uuid to generate a continuation token, and storing a copy of the results from the API. Subsequent calls that use the continuation token, would take a subset of these results. This requires storing more state on the server, and managing that state. The benefit to this approach is that results you get back from paging are consistent. This solves the issue, where the results from the API change while you are calling the API multiple times. The downside to this approach is that you have to store more state in server. If you are storing the full results for all of these paging API calls, then this could be quite large.