Unfortunately, the Firefox Sidebar only accommodates one "page" at a time, whether that is Bookmarks, History, Synced Tabs, or an add-on page.

Can you find a place on the main toolbar where the Bookmarks Menu button will be positioned conveniently for dragging/dropping? I mean this optional button -- -- you can add using the Customize panel (Customize Firefox controls, buttons and toolbars).

Yes, I have placed that button there. I can open its drop-down menu and drag a bookmark out of it which makes the list disappear, then drag to the tabs and drop there. Good. This answers half of my question. However, when I try to do the reverse by dragging a tab up to the button the bookmarks appear, but it doesn't allow me to drop a tab there. Any other way to do this?

Yes, it's a bit fiddly to hover the button until the menu opens, slide the mouse to where you want to add the bookmark, etc.

When you are dragging a tab, I guess it is not the active page?

If it's the active tab, you could try an add-on which you use by right-clicking the folder where you want to bookmark the current page: https://addons.mozilla.org/firefox/addon/bookmark-tab-here/

I'm not sure why you can't drop the "tab" there; must be some difference between native tabs and add-on tabs. Does right-click > Bookmark Tab work on Tree Style tabs?

The tab being dragged can be active or not. Both fail. Yes, you can right-click > Bookmark Tab > Bookmarks Toolbar and follow the menus to the folder where you want to place it, then click Save. No choice as to where in the target folder to place it, unfortunately. One other workaround is to select a tab, copy the URL from the address bar, click Bookmarks Menu, then choose where to paste the tab in the desired folder. Both of these options are OK for one-off bookmarking but too difficult to do for regular use, of course.

That's it, I guess, unless you think of something else. I conclude that this is Tree Style Tabs fault. Unfortunately, TST is a must have extension for me. If there is no solution, then I regret to say that I will have to switch to a different browser. Thanks for helping me to work through this. Onward and Upward. 8-)

I'll be curious to hear how other browsers handle it.

I am taking a look at Vilaldi. Bookmarks and tabs can be in side-by-side panels using Tree Style Tabs. I am still figuring out the drag & drop rules but it looks like this will do what I want. Time will tell.