Firefox: Tree Style Tab interoperability

I'd love to [use this extension on Firefox](https://github.com/cxw42/TabFern/issues/100), but I happen to use the Tree Style Tab (TST) Firefox extension, and the two extensions don't interop out of the box.

The biggest blocker is that the TST tree structure isn't saved when you save a window with TabFern. When you restore the window using TabFern, the tree is either completely flat, or just oddly organized. I think the TST developer already describes how to fix it: search for and then click on "compatibility with session manager extensions" in the main README: https://github.com/piroor/treestyletab

Another issue is that using the mouse to move tabs within TabFern's window messes up the TST tree structure. Ideally, it should behave identically to using the mouse to move tabs within TST's tab bar (in other words, moving a tab should also move its entire subtree with it).

Relatedly, it would be wonderful if the TabFern window graphically mirrored TST's tree structure.

Here's a link to the documentation for general interop with other extensions: https://github.com/piroor/treestyletab/wiki/API-for-other-addons

Start with the Tree Style Tab README section on “compatibility with session manager extensions” and its API documentation, then inspect TabFern’s save/restore and tab-movement handling. Done means preserving TST’s tree when windows are saved and restored, moving complete subtrees consistently, and mirroring the tree structure in TabFern’s window view.

Written by the indexing model from the issue text.