How do I shut off Private browsing mode on my ipad

The method of accessing Private Browsing differs between iPadOS13/14 and iPadOS15.

These instructions relate to iPadOS13/14 only - as the support page has not been updated for iPadOS15:

Turn Private Browsing on or off on your iPad - Apple Support

The method used to access Private Browsing has changed for iPadOS15. To access Private Browsing in iPadOS15, it is necessary to first summon the Safari Sidebar using the button at upper left of the screen [1] - and from the menu tap the Private toggle button [2].

To return to regular browsing, tap the sidebar n Tabs button, that appears above the Private button.

The steps in the support document apply to iPadOS 15. Turn Private Browsing on or off on your iPad - Apple Support

You can do it the other way through the side bat too though.

Follow the steps in the support document you posted from: Turn Private Browsing on or off on your iPad

It explains exactly what you need to do.