Ok, so I fixed this. I had to go to this page: https://pixelrepair.withgoogle.com/udfps with my device in fastboot mode (turn it off, then hold down volume and turn it back on).
Installing the software from there and then manually re-starting my device fixed the problem.
However, for the above website to work, I had to use Edge (Chrome would also have worked as they're the same browser under the hood, but Firefox did not work) and I first had to get Google's USB driver from here: https://developer.android.com/studio/run... (unzip this somewhere).
To install the USB driver, put your device into fastboot mode and connect it to your PC. Then open up Device Manager (Win+X=> Device Manager). Right click on your Pixel 6 and click "update driver". Click "Browse my computer for drivers" and point it at wherever you put the driver. The driver should install and then you should be able to go to https://pixelrepair.withgoogle.com/udfps and install the software (don't forget to reboot your phone once it's done).