Sideberry feels like a better Tree Tabs.

And Tree Tabs felt like a better Tree Style Tabs (but there were no bugfixes in past 4 years).

Though very rarely Sideberry looses/forgets the tree structure of tabs, and I have to restore it from one of the recent snapshots (which it creates every day automatically).

I've tried to switch from TST to Sidebery twice and both times hit small but bad bugs (restore not working on browser restart) and went back to TST. It's simultaneously slicker but buggier. It looks like Sidebery is still under development though: https://github.com/mbnuqw/sidebery/issues

I also had bugs years ago, now I have it make snapshots every hour or so as backups (but didn't need them yet)

Am I doing something wrong? Every time I try to move something into a group, it just gets deselected and I have to select them again and then sometimes it works to move into a group.

you select (how this works depends on your settings, I do shift or ctrl + click), right click, group.

but most useful is the auto-grouping of child tabs anyways

Yes, making groups was easy but moving tabs to groups only works every other time I do it. Very strange.

indentation matters (left and right) if that's a problem

I was also going to recommend Sidebery - I switched to it from TST a while back and I've been very impressed with it.

Yup. Sidebery is now Firefox’s killer feature. Won’t live without it.