this is a well-known new feature request for the PC/website version. You can scroll thru prior requests to find a couple tickets already open. i use the work-around above. Here's one: https://mydramalist.com/discussions/suggestions/33722-sort-watchlist-by-date-added
But note, the first step in solving it has already been taken via the new phone App. Install the App, then look at your Completed list and click on the three dots in upper right corner. Click on sort by List Updates and you are all set. The only thing that would make it more perfect is if they included the date as well. Its been requested, not sure if they have decided to add it or not.
In the meantime, you can see the date when you use the widget function on the PC platform.