We currently export data for a single task in SuggestedEdits.php (the task-preview structure). In addition to duplicating some output formatting (see T308541: Create common serialization method for SuggestedEdits and ApiQueryGrowthTasks), it also means that the user has to wait for the ApiQueryGrowthTasks query to complete before they can navigate the task queue.

That has an advantage of getting up-to-date data (the cached taskset can persist for 7 days) but in case of slow network or network call failure, the user can't navigate the task queue. If T308541: Create common serialization method for SuggestedEdits and ApiQueryGrowthTasks is done, then it is pretty simple to export the full task queue and use the newly created DataStore on the client-side to set the task queue; it can then be reset when the ApiQueryGrowthTasks query completes.