First, apologies for the long post, but I said that I would report back, so here goes. If you don't use a Mac and/or are no longer interested in the double Tab Bar issue, then please feel free to skip this post, but I hope this helps to clarify the issue for some people.
The Dock Preference "Prefer tabs when opening documents:", when set to "Always" will cause Tab Bars to be created automatically and new stacks will be created within the window of the currently active stack, each occupying it's own tab.
When set to "Manually", Tab Bars are not created Automatically and new stacks are created within their own floating window. This would be the most preferred setting as Klaus suggests.
When set to "In Full Screen Only", Tab Bars are created Automatically as each new stack is added while a stack window is open in full screen mode, but not while a stack is in a floating window. If multiple stacks are created in Full Screen Mode they will remain in Tabs when exiting Full Screen Mode.
The problem appears to be that the commands for "Show Tab Bar" and "Hide Tab Bar" do not show up in the IDE View Menu consistently. i.e. "Show Tab Bar" and "Hide Tab Bar" do occasionally show up in the view menu regardless of the above settings, but never on two consecutive occasions, or at least not in my tests or some other users experiences. So if a user sees "Show Tab Bar" in the View Menu and chooses that option either intentionally or not, the "Hide Tab Bar" rarely shows up in the View Menu when it should, if ever, leaving the user stuck with a double bar at the top of their stack and no reliable way of closing the extra (Tab) bar.
Because of the inconsistencies in the IDE View Menu with regard to the Tab Bar options, I feel it is just about impossible to create a reliable recipe for this issue beyond the above explanation.
After spending some time trying multiple tests, I feel the problem is due to the fact that LiveCode generates it's menus on the fly and something in that process is interferring with the fact that the OS also needs to generate the View menu on the fly, most of the time LC wins the battle, hence no Tab Bar options, but occasionally the OS wins the menu battle, then the confusion arrives! That's just my simplistic view.
By adding custom shortcuts for "Show Tab Bar" and "Hide Tab Bar" in the OS System Preferences > Keyboard > Shortcuts > App Shortcuts, it is possible to control the Tab Bar regardless of the Dock setting, but this has a small caveat, it doesn't work the first time you apply the shortcut directly after accessing the View Menu, however, if you try again it does work. The shortcuts don't always show up in the View Menu, but they do work, most of the time, just make sure they don't clash with existing LC or System shortcuts. I used alt-cmd-[ and alt-cmd-] and they worked fine.
I couldn't re-create any issue with a simple standalone app generated from LC even with a View Menu. This may be different if the Standalone creates new stacks, but I didn't go that far with my tests.
Q: Does the Tab Bar have any uses? Well possibly. If you can reliably control it, it is possible to have multiple Stacks open in one window, so it could be useful where you may need more than one stack open, but only need to access one stack at a time, just another option. It maybe a tidyer option than having say three floating windows and having to figure out which is which stack - maybe. One big drawback is that the Script Editor opens up in a Tab of the Stack when the Dock Pref is set to "Always", that didn't feel very useful.
One thing that is missing that other apps do have is a "+" symbol at the right hand side of the Tab Bar for creating new empty tabs, I'm not sure how this would be useful in LC though, maybe creating a new empty stack within the window.
I also tried a small experiment by creating 3 stacks of different sizes and added a button in the bottom right corner, the button was set to stay in the bottom right corner when the stack was resized. When joining all three stacks into one tabbed window (by drag and drop), the buttons did stay in their correct relevant position, so joining stacks into one window using their Tab Bars does appear to respect the Geometry Manager.
So to the final point, is this a bug? I would say probably not, but it could be implemented much better, especially if the commands would show up in the View Menu consistently. I feel that the bug is the missing commands from the IDE View Menu for controlling the Tab Bar, if that could be fixed I'm sure there would be a lot less confusion.
After all this work, at least now I can reliably and consistently control the Tab Bars, I hope some of you can too.
Paul