The Safari side panel , in iPadOS 15, is now open and closed with the side panel, small rectangular icon, at top-left of the Safari main menu bar.
For this button to be visible and work, when the Bookmarks/Reading List/History option is displayed, you must first tap the Back arrow and then, the “Safari” name button that appear in the upper left corner of Safari.
You may have to tap the back button as many times as necessary to get back to this point of being able to tap the “Safari” name button to dismiss the Bookmarks panel.
If you hate this new “feature” as most everyone else has, who has posted about this, you can make your voice heard to Apple by posting feedback about this issue in the feedback link below.
Tap the link below.
https://www.apple.com/feedback/ipad.html