The key statement in the alert is:
This macOS system error message is slightly misleading. As with most sandboxing restrictions, it's not you (the user) who does not have permission; it's the app (Nisus Writer) that is being denied permission.You do not have permission to run the application "Nisus File Converter.app"
NSCocoaErrorDomain code 257
This is a system bug:
This error is new to recent system versions, but is found in both macOS Catalina and Big Sur. The problem seems to impact all kinds of helper apps, not just Nisus Writer. Apple recently acknowledged the issue in this support document on scanners.
MacRumors reports that apparently Apple will fix the problem in a future system update. Hopefully Apple makes good on that statement.
How to quickly bypass the error:
To quickly ignore the problem you can click the "Retry" button in Nisus Writer Pro. That will use a backup converter built into macOS. However, be aware that this backup conversion is less thorough and will omit special content like styles, comments, footnotes, etc.
How to completely workaround the bug:
You can bypass the issue by manually launching the converter app. You only need to do this once. Afterwards the system should continue to allow the converter to be launched automatically by Nisus Writer as needed. Please take the following steps:
1. Quit Nisus Writer if it is running.
2. Select the Nisus Writer Pro app in the Finder.
3. Right-click it to show the contextual menu and choose Show Package Contents.
4. Open the subfolder Contents/MacOS.
5. You should see the Nisus File Converter app; double click the app icon to launch it.
6. You will need to quit the running converter app, but it's invisible as a background app. You can either:
6A: Reboot your entire Mac -or-
6B: Launch the Activity Monitor app, select the Nisus File Converter in the listing, and choose to quit it.
You should now be able to relaunch Nisus Writer and convert files without errors or interruptions.
This fix will remain in place for the current version of the app. You will not need to repeat the fix after restarting your Mac or quitting the app. However, you will need to repeat these steps any time you replace the app on disk, e.g. after downloading a new version.