Installation instructions are confusing and mixed up at the moment with roms for android 11 and 12 requiring different steps to flash a recovery.
If you want to install eOS-s please install google’s stock android 12 first. Also read this post about similar problems on another pixel device. It’s best practice to put stock on both slots before flashing eOS.
Then to flash recovery on android 12 pixel choose the oldest vendor_boot.img from the list. It may or may not work, I don’t know for sure. There have been problems with this recently.
If that doesn’t work you may try to extract the vendor_boot.img from the payload.bin of the eos rom you are trying to flash. Again, I don’t know this would work but think it may. Payload dumper helps to do this.