You can learn about adding Widgets to both your Home Screen - and Today view - here:
> Add widgets on iPad – Apple Support
> Use widgets on your iPad - Apple Support
Having updated to iPadOS15, you would be well advised to review the iPad User Guide - as this comprehensive source of information about your iPad and iPadOS is often overlooked. The User 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
With iPadOS15, you are now able to freely position widgets on any of the Home Screens - but you have lost the perhaps familiar “compact” first Home Screen layout that shows a compressed 5x6 grid of App/Folder icons and Today view in Landscape screen orientation.
Widgets placed on a Home Screen now individually occupy one or more elements of a 4x6 icon grid. Home Screens without Widgets retain the familiar 5x6 icon grid. The slide-over Today View, previously seen in Portrait screen orientation from the first Home Screen, is still present - and is now also seen in Landscape. However, slide-over does not incorporate the Time and Time panel. For iPad mini, the available grid has fewer grid elements.