Is there a similar product I can use to re-arrange taskbar tabs?

I don't think so. I'm not familiar with any alternative for Windows 7 and up.

Several antiviruses disallow running apps from the AppData folder. You can try the following:
1. Try installing the tweaker to the Program Files folder. You need to run the installer as administrator and choose the Program Files folder manually during installation.
2. Try the portable version of the tweaker. See the FAQ for instructions of extracting the portable version.

I tried to reproduce it with Notepad both with a click and a mouse wheel, both on Windows 8 and Windows 10. I couldn't reproduce this.

Just tell me how you customized the left click. If you're saying that it happens without you customizing the left click, then it probably happens when the tweaker is not running, too. Is that right?

Attaching the relevant screenshots:

As far as I understand, you'd like to be able to have this:

Let me know if I misunderstood.

What's your setup? How can I reproduce this?

There are no non-advanced options related to the left click. So please provide your relevant advanced options, and I'll see if I can reproduce it on my computer.

I couldn't reproduce it. What I tried:

• Open and maximize Notepad.
• Minimize it.
• Set "Middle click" to "Switch to".
• Double click on the Notepad taskbar item with the middle mouse button. (1)
• Minimize Notepad again.
• Check "Minimize/restore when mouse is over: Taskbar buttons".
• Restore Notepad by scrolling up aggressively. (2)

During my testing, in steps (1) and (2) (and in general) Notepad never became restored, only minimized or maximized.

I mean if I cycle through windows I'll end up with all windows restored, cuz it's restores ech window one by one.

I mean, a difference between using "Combine taskbar buttons" -> "Always, hide labels" and setting all of the taskbar items to hide labels using taskbar inspector.

And all unnecessary windows will be restored instead of being still minimized.

If you click once, only the last active window is restored. (Maybe you're using "Restore all group items"?)

The unused windows for some reason are forcing themselves to be restored instead of the recent one.

Perhaps your specific app works that way. You can try it with another app such as notepad and see that it restores one window at a time.

And why "Switch to" command for combined items works as thumbnail preview instead of switch to recent window?

That's how it's implemented. It's true for all options - "Switch to", "Minimize", and "Close". I can consider adding a new value to taskbaritem - "Cycle through windows".