According to the latest information, in Android 13 QPR2 Beta 2.1 a new bug has now started occurring. It is crashing a Pixel Launcher search if you attempt to scroll through the results.
Apart from it, if you just enter a query and tap an app from the top row of results or one of the first few Google Search suggestions, the Pixel Launcher works normally.
Scrolling down to see other things from the web or the “From your apps” section (Settings, Play Store, and YouTube/Maps search shortcuts) will remove the query you just entered and close the keyboard – 9To5Google.
The issue is currently occurring on QPR2 Beta 2.1, but not Beta 1.