Possibly stupid question: So an Admin role is on the Classic Center and that can't be changed. And you can't edit the tabs within the Classic Center. But what dictates what order the (custom) tabs show up within the Classic Center? If I install a bundle that adds a tab to the Classic Center, is it just being added to the right as the newest tab? That doesn't seem right, but I can't make any sense of the order they are showing up in.

I think the developer can choose an Insert Before setting if they want. If that is blank it is populated at the end (right). Otherwise it is placed before the selected tab For example SPS commerce is installed first in the menus so I believe they chose to insert before Transactions tab