Your comments

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:

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.

Well, if the problem happens without the tweaker running, it sounds more like something 7tt does on initializing fixes the problem... Also, indeed it can also be related to StartIsBack which touches this area. I'm closing this issue for now, as it seems to be unrelated to 7+ Taskbar Tweaker. If you find something else, or come up with reproduction steps, follow-up with a comment.

Can you please upload your explorer.exe file? You can use a service such as

explorer.exe can be find in the C:\Windows folder.

The standard menu is a Windows feature, and can be activated by holding the Shift key (7+ Taskbar Tweaker merely allows to use it without Shift). I'd assume that the bug is unrelated to the tweaker and happens without it if you try to bring up the menu with Shift+right click.

    You see in my answer in the topic you linked why it's challenging and cannot be perfect, unless it's implemented with the help of a Chrome extension, in which case it will a Chrome-specific solution.