I seem to have solved this.
Extensions are identified by the file extension .appex and are are fetched from the app bundle on first launch, appearing in the Extensions pane of System Preferences (System Settings or whatever it's called in modern macOS) where they can be enabled or disabled with a checkbox - as I'm sure you know.
When the app is uninstalled, the app's extensions are still offered, rather annoyingly. Let's fix that now.
Before following the procedure below, close System Preferences to avoid issues.
The best way to to find those pesky extensions and delete them completely is to locate them with something like Thomas Templeman's excellent Find Any File. Search your User folder for the name of the extension, inserting dashes in place of spaces for the closest match. You may want to verify the exact name in the Contents/Resources/Library/Plugins folder inside the app bundle, looking for the .appex file extension.
For a sandboxed app you'll find the files your'e looking for as named folders in ~/Library/Containers/ and ~/Library/Application Scripts/
Example search results from Find Any File
In both cases what you'll see is the standard reverse URL for the developer and app used as the name of a folder. Trash these. In Find Any File you can do that from the results window, or double click on the item of interest and it will be opened in the Finder.
To the best of my knowledge, both these folders can be deleted without creating issues with a related .db folder - to the best of my knowledge it's simply a case of "It's not there, it won't be loaded".
If you searched you entire drive, you'll see similarly named folders deep within /private/var/folders/ but these need not - and therefore should not - be deleted. In case you accidentally did delete those, or anything else you shouldn't, make Finder active and hit Cmd+Z to undo.
Now you can reopen Extensions in System Preferences and enjoy no longer seeing redundant finder extensions offered.
In my case this procedure was necessary because using a particular Share Menu extension was freezing Finder, necessitating a force quit (and re-spawn) of Finder. I didn't want to run the risk of accidentally reenabling the extension later, as I still use the app. And, yes I'll let the dev know.
Lastly, I deleted the offending extension from Contents/Resources/Library/Plugins/ inside the App package. Upon relaunching the app, the buggy extension wasn't loaded by macOS and didn't appear in System Preferences.
This is a very important step if, like me, you still have the offending App in your Applications folder.
If you don't delete the offending plugin, the extension will reappear in System Preferences even if you don't relaunch the app because it's been added to the above locations again. Clearly there is a db somewhere telling the OS to scan apps for plugins (which doesn't purge them even when the app has been deleted). This may cause issues for others but it hasn't in my case. And take care not to "Undo" the deletion in Finder, as you won't see it happen unless you have the app bundle open at the time!
A note of caution I've seen some very well respected folk telling people not to try and delete Extensions at all. I respect their expertise and fully understand why they say this. But my hands-on experience is that it is both possible and safe to do in the case of redundant third party extensions, following the procedure above.
YMMV
