Good idea. Fixed in next version. 

Yes, in some cases they must slide in order to keep the tabs in the same order in the tabbar (horizontally) as they appear in the page tree (vertically). This is done because it makes ctrl+tab and closing tabs work more intuitively, and also helps Sidewise work properly together with other extensions such as session manager extensions.

The easiest way to intentionally cause the sliding behavior is by dragging a page row in the tree to a new location in the tree -- the tab will slide on the tabbar to match that movement.

In general, ctrl+tabbing through your tabs should also advance the row-highlight through the tree in sequential, top-to-bottom order. If the row-highlight jumps around in the tree when doing this, then Sidewise isn't working right. Please let me know if you see this happen.

Do you find the sliding that still happens annoying? I ask because I am considering making this "keep in same order" functionality optional in the future.

Please see my response to this question in another Userecho thread.

I am tentatively planning to add this as an "in pane" option. Most likely by adding a dropdown arrow-box next to the search box, and clicking to show a menu which includes (among other things) a "Hide hibernated" option.

I like this idea but I'm concerned about horizontal space in the sidebar and having the (# open, # hibernated) stat run off the right edge of the sidebar pane for many users. I'd like to come up with an intuitive abbreviated format like (# O, # H) though that particular example isn't terribly intuitive.

This should be possible once the "Recently closed" pane is in place. This will likely change the "remember open tabs between sessions" behavior to something more like "remember previous session windows in pages pane", and if unchecked will migrate previous-session windows to "Recently closed" instead of keeping them around in the pages pane.

The "Set label" context menu item will currently do this. Marking as PLANNED to probably change the label to "Rename folder" when only a folder is right clicked.

I would like to do this but I'm not sure I have a way to detect a crashed tab specifically. Will investigate.

Yeah it does normally; that's one of the problems I need to resolve before releasing this script "proper". Minimizing/restoring is a little flaky all around with the script running at the moment. 

Fortunately an enterprising user has sent me some bits of code for the script that should correct this.