Duplicati completely stuck

Click the link for an explanation if you like, however it sounds like you aren’t using that option.
Snapshot is used to backup locked files by getting a “frozen” image of file data at that instant.
This can cause a noticeable delay, although I believe it’s usually just minutes unless it breaks.

“De beworking List is afgerond” is “The operation List has completed”, but I see no files count.
What other Duplicati things that use this connection are giving results showing “working fine”?
The other odd thing about your list operation is that it did two. Normal operation would do one.

Possibly it’s decided it needs some repair work, but the logging level might not be showing it…
Manually running a Database Repair (after a Duplicati kill and restart) might be a relevant test.
Manually running a Database Recreate would try to recreate database from backup if possible.
Deleting the backup and starting again would be another way to avoid any old lingering issues.

Do you refer to Duplicati’s Process in Task Manager, or Tray Icon right-click then quit, or what?

If you mean that the Stop button can’t stop the “Backup is starting”, that might be expected (but undesired) behavior when things are stuck. Although it’s a bit risky to the database health, Task Manager Details “End Task” should be able to kill all the Duplicati processes (probably just two).

If you’re trying to delete the backup job, you’re probably seeing the request get queued until the Duplicati server finishes its current backup - which isn’t finishing. Many things run one-at-a-time.

If you want to start clean, you can kill Duplicati, restart it, go to the job’s Configuration → Delete, checkmark “Delete remote files”, and answer the CAPTCHA. You can then Export your working configuration for the NAS, Import it for STACK, then change configurations a necessary for that.

https://forum.duplicati.com/search?q=stackstorage finds sample configurations others have used.

Before doing all that, it might still be worth looking at the live log Profiling view as was mentioned.
That’s almost as detailed a view as is possible. I don’t have STACK, so can’t test things for you…