You’ll continue to see changes roll in over the coming weeks. For now, the big change is making suggested templates available in your doc list.
You mentioned that the templates stay open in your doc list. If you want to hide the list, you should be able to do so by clicking on the second button in the list - it should read “Hide templates”.
If you create a copy of a template, you should see your own copy in your doc list. If you no longer need it, you can always delete it.
If this isn’t what you are seeing, can you send me a DM with a screenshot of the issue.