The Google App beta version has received a customizable search bar widget, something which has been available in third-party launchers for quite some time. Now that Google is officially adding this feature into the widget for the stock launcher, users will get access to a handful of options that will let them personalize their search bar widget to their own liking. This includes thing like changing the shape as well as adjusting the color to something that better matches the colors of the home screen wallpaper, which is probably a nice touch for users as something similar is available in Action Launcher thanks to the color picker.
You'll need to be on Google app beta version 7.14.15 to see the feature pop up, though it is worth noting that after some testing with the latest version, it didn't show up as expected, so it's possible that not all uses will see it even after the APK is installed (which you can grab from the button below if you want it), and it's likely obvious but you'll want to be using the stock launcher and not a third party one, or at least not a third-party widget.
Once you have the correct Google app beta version installed, if you place the widget for the Google search bar on your home screen you should see a new overflow menu (the three dots button) at the right side of the widget. Tapping this will reveal a drop down box with two options - customize, and send feedback. The customize option is where you'll find things like the the shape of the bar if you want it to be more rectangular or have rounded sides. You can also change up the logo that you see at the left side of the bar, and of course there's the color options, which lets you switch between white, black and white, inverted, or the color picker which, just as with Action Launcher will pull colors from the wallpaper background on your home screen to match up with it nicely. There's even an option to set the transparency of the widget if you want to make it a little more see-through. Eventually this will be an option that rolls out to all users even on the stable version of the Google app, but for now you can install the beta and you should have access to it.