How to find replacements for Dashboard widgets in macOS Notficiation Center
For the record, I've updated to macOS Catalina now.  The Notification center now has an "App Store" button that takes you to Apple's AppStore, where there is a section for Notification Center Widgets.  Although the selection is somewhat limited, it's nice to see a small collection of widgets.


Although there is no widget to replace the dictionaries I described in the original post, it is not hard to use ⌘-Space to quickly get Apple's Dictionary App.  It is pretty straightforward to add various foreign language dictionaries to that application.

All in all, it has been possible to replace the features I liked in the discontinued Dashboard with Notification Center Widgets and other applications.