Are any of these known issues? (Xavron June 2021 edition)

With Duplicati.GUI.TrayIcon, you can double-click or use right-click menu to get it to open in the browser.
I don’t use Linux much, but systemctl start duplicati seems to launch Server not TrayIcon, so I suppose one needs to know the URL. Some people may run a TrayIcon with --no-hosted-server to have something nicer to drive. I suspect TrayIcon isn’t the systemd default because not everything has a GUI
(e.g. headless servers), and even if they have a GUI, it’s not clear that a background process can use it.

There is a concern that setting up a Windows service with TrayIcon is hard. Same may be true for Linux.
Duplicati has multiple components, and things like a Windows service or systemd server can’t get to UI.
I don’t know if there’s a good way to improve all of this, but whatever it is would need someone to build it.

systemd does this part. It will run scheduled backup whether or not you open a browser to interact with it.

The Linux installation instructions leave a lot to be desired, as noted in Part of installation fails on Ubuntu, which may or may not result in any changes in the manual. Somebody has to either write, or help author.

Windows fares slightly better on the TrayIcon setup. See Configuring the Duplicati Tray Icon in Windows, which is somewhat odd because the default Windows installer sets up TrayIcon including internal server, started at login. Many people are happy with this. Linux is somewhat more do-it-yourself about setting up.

I had thought one needed to systemctl enable duplicati, or at least the manual now suggests it.

Which do you want? Please check your Duplicati environment as shown to see what $HOME it sees.
I can’t think offhand how systemd would set things up wrong. Are you sure that’s start from systemd?
systemd status duplicati should show if it started it. systemd restart duplicati to be sure…