Pixel Launcher will soon allow you to choose the default web 'Search engine'.
The app build that comes with Android 14 QPR2 Beta 3 contains a hidden search settings item called "Search Engine". This feature will allow you to choose an app for the web search.
Screenshot from the linked tweet of the setting in Android 14 QP2 Beta 3:
Thats good to hear. Thanks for checking. Graphene OS team did an amazing job with their OS.