This is what I see if I go to Page Elements to edit the Links widget:

No widgets! To get the widgets to re-appear you have to:
1. Design>Edit HTML>Copy existing HTML
2. Old Templates>Revert to Classic Template
3. Customize Design>Upgrade Your Template
4. Select Template [Watermark]
5. Edit HTML>Paste existing HTML
6. Page Elements [widgets re-appear]>Links [which you can then edit]
Of course, there is nowhere online that sets out these six steps, but trial and error eventually led me to the discovery that this will make the widgets re-appear: fraught trial and error, since there is the ever-present danger of loosing everything in your blog.
Having gone through these six steps again I have added a few more links. Thanks to J. for the two great mid-century design blogs. The others are bookmarks I have accumulated looking for materials for the house. I will add another batch when I am feeling particularly brave!