Okay, so there's a couple of routes you can take regarding the browser:

• A resource efficient setup, so you can keep 5000+ tabs open without your system slowing to a crawl (category A)
• Bookmarking tab trees such that the structure is stored (category B)
• Utilizing sessions such that the tree structure is stored (category C)

Category A

I wonder if Pale Moon can handle 5000+ open tabs. I've never tried it in that browser, but if memory serves me right, the old Firefox was actually less resource efficient than the newer ones. And you seem to have rejected this option anyway. It could still be worth a try, you never know how it turns out in practice. I know of a lot of addons for Pale Moon, which you can get through the Classic Add-ons Archive, which archives almost 20,000 add-ons. If you want to, you tell me what you're missing in PM and I'll see if I know of any add-ons that serve that purpose. (If a lack of features was the problem of course.) Especially "Tabs Tree" is a well-programmed add-on, much more lightweight than the add-ons available for the modern Firefox.

Another lightweight browser that supports tab trees is Falkon. I haven't used it too much, but based on the little experience I've had with it, I'd recommend it. Only if your needs are simple, though. It doesn't have many add-ons, but it does have the essential ones such as an ad blocker and a script blocker.

A few resource efficient add-ons for the modern Firefox are Vertical Tree Tabs, Power Tabs, and Tab Sidebar. Only the former supports a tree proper, while the latter two provide vertical tabs with grouping functionality (effectively a tree with a depth of only one level, with the possibility to collapse / expand those groups). Power Tabs lets you make folders in which the tabs are grouped, while Tab Sidebar automatically groups the tabs that are opened from middle clicks. This works well with Simple Tab Groups if you want to better organize your tabs. This is my current setup.

Category B

The solutions I mentioned above are recommended. The problem with the following add-ons is that they make the browser slow, are buggy, or both.

There are two add-ons in category B: Tree Style Tab and Tree Tabs (not to be confused with the obscure Tabs Tree I mentioned above). TST is the best for this, because it preserves the tree structure. Tree Tabs will create a folder with one bookmark for all tabs in the sub-tree, but when you open it, it will just be a flat list. I've experienced bugs with TST, but not many and nothing that can't be fixed. The problem is that it makes your browser slow. Tree Tabs also makes your browser slow, but not as quickly as TST. It does have a bug where all your groups get merged into a single one, and I believe your tree structure also gets lost when this happens. YMMV, maybe it won't happen to you.

Category C

You can't just use any session manager with a tree tabs add-on, because it won't preserve the structure. The add-on should have a built-in session manager.

Tree Tabs falls in this category as well, as does Sidebery. The latter can also store your session automatically. And it doesn't make your browser slow! I would recommend it if it weren't for this fatal flaw: it also has a bug where your groups get merged into a single one, and IIRC the structure gets lost. Yep, just like with Tree Tabs. Again, maybe it's something about my setup that causes this and you won't experience it. Or maybe it's been fixed by now – I haven't used either of these add-ons in almost a year.

Overview

I'll just summarize the above quickly to give a better comparison.

Well programmed solutions but with fewer features

• Tabs Tree (PM / WF)
• Falkon
• Vertical Tree Tabs (FF / WF) (Can be combined with Simple Tab Groups)
• Power Tabs (FF / WF) (Can be combined with Simple Tab Groups)
• Tab Sidebar (FF / WF) (Can be combined with Simple Tab Groups)

Solutions with more features but which are heavy / buggy

• TST (Can bookmark trees and be combined with Simple Tab Groups)
• Tree Tabs (Can bookmark trees, and has groups and a session manager built in)
• Sidebery (Lightweight but buggy; has groups and a session manager built in)

Further mentions

Finally, there's an add-on called OneTab, which will aggregate all your open tabs into an overview page, and then close them. You can do a little tab management in this overview page. Namely you can organize them into editable groups. Handy, but it won't save your tree structure.

Let me know if this helps.