You would appear to have the iPadOS16 Stage Manager function enabled on your iPad. Enabling Stage Manager modifies available multitasking views…
With Stage Manager enabled, you will see the new Windowed UI (User Interface) - and with it you’ll see the multitasking options that you describe.
With Stage Manager disabled (arguably, this being the far more useful mode when using the iPad without a connected external monitor), you will see the established Full, Split and Slide-over views listed and accessible from the three-dot button.
Stage Manager can be disabled (or enabled) from iPad settings:
Settings > Home Screen & Multitasking > Stage Manager > Use Stage Manager on iPad - set to OFF
The Stage Manager feature can also be simply enabled/disabled from the Control Centre.