How can I backup/restore the system tray layout?

I have a Dell Latitude 7490 laptop which is normally connected to a docking station using USB-C. The docking station is connected to two monitors which each run a resolution of 1920x1200. The built-in monitor runs 1920x1080, but I don't use it when connected to the dock (lid is closed).

I have the the task bar set up "Vista style" with the quick launch tool bar, buttons with text and the clock in the system tray displayed on one line (no date showing). This works fine both when using my external monitors and when using the built-in monitor and no external monitors. The problem occurs when I start my computer and use the built in, then plug into the docking station to keep working on the externals, now my taskbar is wide, the clock is displaying on two lines, with the date on the first line and time on the second. I need to log out of
Windows and back in in order for the taskbar/tray to look right again.

I have tried restarting explorer.exe, but that in itself does not work, a complete logoff/logon is required.

Is there a way to backup the settings when the setup is to my liking and so I could just import a .reg file to get it back? Or, are there other, better solutions to this problem? I'm attaching two images in case my description was not sufficiently clear. Any help appreciated!

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Thank you for the suggestion. I've already tried this but it does nothing for me. It seems to have to do with pinned apps, a feature I don't use (I use the quick launch).

Thanks again. It seems you are doing the same Google searches which I did before posting (as you can see from my screen shots I've added the very ShowSecondsInSystemClock value that you mention).

I tried exporting the entire HKEY_CURRENT_USER\SOFTWARE\Microsoft\Windows\CurrentVersion\Explorer branch in the good and the bad state and compared the two files using Notepad++, but I can't find any interesting differences. So sadly, I'm still not helped.