How to turn off private browsing on iPad

Tap Start Page.

If no change and your open tab is still operating in Private Browsing mode, close Safari - then perform a forced-restart of your iPad:

• On an iPad with a Home button: Press and hold the top button and the Home button at the same time. When the Apple logo appears, release both buttons.
• On other iPad models: Press and quickly release the volume up button, press and quickly release the volume down button, then press and hold the top button. When the Apple logo appears, release the button.

Presumably you refer to the native Safari Browser’s Private Browsing mode?

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

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.

That’s the only way. Do you see “## tabs” under private? Tap that

See the related article above

You are very welcome. I’m delighted that the problem is now resolved.