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:
Just for anyone looking how to do this, you should have your default web browser set to Firefox (settings -> apps -> default apps) then swipe up from the home screen, search for the "Google" app, tap your profile picture in the top right, and go to settings -> general -> uncheck "Open web pages in the app."
I started with this, but I have trained myself to use the search bar at the bottom of the home page as the beginning so often. That automatically opens Chrome regardless, unless you switch launcher.