As described, I suspect that you make reference to the “Shelf” - this being a new feature of the now revised iPadOS multitasking environment.
iPadOS permits you to have multiple “instances” of the same App - each instance being self contained with its own open tabs. The shelf, when triggered, does not show your browsing history - but instead shows a thumbnail of each running instance of an App.
For example, if you have three running instances of Safari, each with its own set of open tabs, you will see three thumbnails corresponding to each running instance of Safari - plus a button to open a new instance of Safari. Simply tapping a thumbnail will switch directly to that running instance of Safari. Each App has its own corresponding shelf.
This article from Appleinsider has a useful explanation of this new feature along with many of the updates to multitasking:
https://appleinsider.com/articles/21/08/12/how-to-master-multitasking-on-ipad-and-ipad-pro-in-ipados-15
The iPad User Guide is also a rich source of frequently overlooked information. The Guide is available both online using a web browser (such as Safari), or as an Apple Books download:
iPad User Guide - Apple Support
https://books.apple.com/book/id1567104892
You should note that the shelf is an integral component of the multitasking User Interface. It cannot be disabled.