You can find the link here:

https://ramensoftware.com/7-taskbar-tweaker#download

Should be fixed in v5.15.1.2 beta. Please try it and let me know if the fix works for you.

remove the Scrollbar that appears when I have more than 1 row of icons in taskbar

What would you like to happen instead?

prevent scrolling into completely blank rows

I never encountered it, but it sounds like a Windows bug. Do you have a way to reproduce this issue?

Is the idea that I should apply this customization when the odd behavior occurs, as a test?

As a test to see whether it's related. Then, once we gather more info, it might be useful as a long-term workaround too.

I guess the thing I should test the next time the issue occurs is: what happens if I close the tweaker, but do not restart it. Does the issue persist, or does it go away when the tweaker is closed?

Yes, that would clarify whether the issue is actually related to the tweaker.

I meant, "stuck" in software, i.e. somehow explorer thinks that shift is pressed.

What I also meant in my previous comment is that you can configure shift+click, and then if you see that action being triggered instead of the new instance action, you'll know that it's indeed related to shift+click somehow.

"is related to something that is happening in the tweaker" - what makes you say that?

You can try customizing the Shift+click event to see whether it's being triggered for some reason, maybe because the shift key gets stuck or something. You can open the advanced options from the tray icon and configure it as following:

What's your 7+ Taskbar Tweaker version? Please make sure that you're using the latest version, 5.15.1.

Perhaps you're holding Shift while clicking? Shift+click opens a new instance, and it's unrelated to 7+ Taskbar Tweaker, it's a Windows feature. If that's the case, you can use the tweaker's advanced options to disable or re-assing Shift+click.

If not, then I'm not sure what the issue is, but I need more details, and preferably a way to reproduce it, to look into it.

To access Advanced Options you have to right-click on the 7+ Taskbar Tweaker notification icon. Then you can change the virtual_desktop_order_fix option.

Note that the order of pinned items isn't remembered as described here:

https://ramensoftware.com/7-taskbar-tweaker-v5-2-with-support-for-windows-10-anniversary-update#comment-7189

Please try the newly released beta version, v5.15.1.1. I can't try it as I don't have Windows Server 2022 installed, but I believe that the adjustments I added will solve the problem.