On what distros/desktop envs is it possible to have the same taskbar on every screen?
I recently installed Linux mint ane was unpleasantly surprised that it is virtually impossible on every desktop environment, as opposed to Ubuntu on which it required very little.
You just add a panel to every screen as it doesn't do it automatically, but if you want a taskbar where the open apps are visible from different monitors on the panel then you could try using kubuntu backports for kde 5 on mint, go with the minimal install. You still need to manually add the panel to extra monitors, but they are linked together.
When you add the main panel on a different screen it saves the app layout exactly, don't remember if it keeps clock the same, but you can add that yourself.
I prefer how cinnamons window manger works better, but kde is awesome so I switched.
GNOME with dash to panel. It allow you to clone it I guess. dash to dock allow you to copy the dock, so only the applications, not the systray.
KDE allows you to create panels on every screen, with the systray. You'll have to replicate them manually (pin the applications or whatever you put on your first panel).
Others DE I tried had flaws for that :
Cinnamon cannot have all the systray on the second panel.
Budgie doesn't allow you to have a panel on the second screen (but you can clone the panel on the same screen).