Actually, that plugin does not do what this feature request is asking for: it cycles through tabs, not tab groups, as it has not been updated to work with Obsidian 0.16 yet.
I would really like this as well. Yes, I can focus on the tab group to left/right/above/below, but then I have to have 4 hotkeys. All I really need is one - to cycle between them. I don’t normally have more than 2, and I just want to be able to easily bounce back and forth between them. I’ve checked out several plugins, but have yet to find one that can do this.