That does sound odd. First, though, “startup” means user login time unless you set a Windows service. Assuming that’s OK, are other things in your startup folder starting? Maybe Duplicati started and died?
--log-file="C:\<path-that-this-user-can-write>" --log-file-log-level=Information
appended to the startup shortcut Target field might show something if it started, then managed to say:
2020-01-18 14:47:20 -05 - [Information-Duplicati.Server.WebServer.Server-ServerListening]: Server has started and is listening on 127.0.0.1, port 8200
and perhaps you’ll see some other errors. If the file isn’t written at all, it either died too fast or didn’t run.
If your system has another account (possibly an admin account, otherwise visibility might be poor), you could set that account up to run Sysinternals Process Monitor to see Duplicati file actions at your logon. Compare the manual start that works with what you see when the at-login startup doesn’t seem to start.