Screen view on ipad
When I open my apps, they’re not full screen and they have a small curve/arc the bottom right corner that I have to touch and drag to go full screen.
iPad Pro, iPadOS 17
Question marked as
The "arc" that you describe is a handle - that you drag to change the proportions of the associated App Window.
As you have discovered, you will only see re-sizeable windows when Stage Manager is active for either the iPad display, or connected external monitor.
This functionality is described within the iPad User Guide - this being a rich source of information and feature guidance for iPad and iPadOS:
Move, resize, and organize windows with Stage Manager on iPad - Apple Support