Duplicati has two steps, “Install” and “Activate”. I’ll refer to Upgrading Duplicati by @JonMikelV (thanks!).
“Install” does the download and install. “Activate” quits the current version of Duplicati and starts the new. Default Tray Icon update should just take those two steps as shown in the How-To assuming all goes well. Download gives a progress bar to view. Normally it’s fast, but if the download fails, “Install” is shown again. Advanced non-default installations such as Windows service currently require a manual restart of service.
MENU → About → General shows the running version, though sometimes a browser refresh is required.
If a Windows (not Duplicati) error popup happens, it might be separate enough that Alt-PrintScreen could capture just that popup to paste in a forum reply with Control-V. If too much got captured, cancel the post.