I can create a new tab group with existing open tabs, but I don't see a way to update the tab group with newly added or renamed tabs. The only option I can find is to manually add each new tab and rename any existing tabs by hand.
Is there any easier way to do this other than deleting the tab group and creating a new one from my modified tabs?
If you load a tab group, make changes, and then go to save it, the name will already be filled in and you just have to click OK or push return to save over the same group to update it with the new tabs.
You can also set up a button, menu item, or hotkey to save over the current group in one click, without any prompt. That'd only be worth setting up if it's something you do really often, but is an option if you need it.
If you're in Preferences then the groups there can be edited directly. (And creating a new group there creates a completely empty group, since it's not connected to any window with tabs open in it.)