Is it possible to have a C# application find all files with a given tag and display them as a set of links and allow editing
First, the language you are using is rather irrelevant as long as you can access the network and open a browser.
I see one challenge to find an API that will return the files of one tag. Honestly, I have not checked the compete documentation. You might need to write a small Nextcloud app that will have access to the database in PHP that provides appropriate API access.
From there on, your c# or whatever program can read the list of files with given tag in form of links. However you present this to the user is up to you.
Finally, the question is how to edit the files. I suspect you mean by the Nextcloud apps installed. You should be able to open a link to the file in the files app. If the file type is one with an editor attached, the user can edit online by opening a browser.
If you want to edit locally without browser, you can download, edit, and upload but might run into conflicts.