I had the same issue. When you drag the group/folder towards the app or vice versa, if they're in a grid, iOS tries to be smart and automatically reorders or "reflows" the apps in the grid. You have no way of communicating your intent to iOS.
The way to solve this is to move the folder somewhere else entirely, where iOS won't consider it part of a grid that needs to reflow. For example, you can move the folder to an entirely new home screen on its own. And then you can drag the new app into that folder, and then move the group back to where it was originally. And then, if you're like me and you want your apps in a specific order, you likely need to manually reorder the entire grid again, because the reflow will have changed everything.
Increasingly iOS is filled with these kinds of "magic" features that end up getting in the way of what you're actually trying to do 🙄