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Bug 2: I could not reproduce the issue. Can you provide exact reproduction steps? A video demonstration can help, too.

Bug 1: I could reproduce this. What happens is that all of the virtual desktops share common data, and that makes things tricky for 7+ Taskbar Tweaker. The decision of whether to group a newly created button depends of whether the existing button is only a pinned item, or contains a button. In your case there are two virtual desktops, and while the existing item doesn't contain buttons in the current virtual desktop, it does contain a button in general. That's why the grouping doesn't take place.

I might look at it one day, but currently it's not a priority.

Do you think that 7+ Taskbar Tweaker causes the issue? Or is it just an idea for something that the tweaker could fix?

That should be fixed in v5.2.9.3, among other things. Please try it.

Когда финальная версия будет готова, будет опубликован пост в блоге.