Exit private browsing does not work

When you are trying to exit Private Browsing, you should be able to tap on the "squares" icon you mention in the upper right of the screen, or the icon on the left side of the screen that FoxFifth provides. Either will work. Once you tap on the squares that you mention, you should see this.

When you tap on Private, you will see this.

Tap where it says 3 tabs, which are the original tabs that you had open. Yours may differ slightly, depending on how many tabs you had opened before Private browsing was opened. That will turn it off.

If you decide to use the icon on the left side as FoxFifth describes, following those steps will work. Again, just tap on the Tab listing and it will get out of Private browsing.

See the following from Browse privately in Safari on iPad - Apple Support (ME)

To hide the sites and exit Private Browsing Mode, tap , then switch to a different Tab Group. The tabs reappear the next time you use Private Browsing Mode.

I'm not sure what you mean by square icon at top right or by exit "v" -- neither are mentioned in my previous reply or in instructions I referenced.

See the following from Browse privately in Safari on iPad - Apple Support

To hide the sites and exit Private Browsing Mode, tap , then switch to a different Tab Group. The tabs reappear the next time you use Private Browsing Mode.

The icon is at top left (not top right). Then you switch to a different tab group ("Start Page" if you have no other tab groups).