Thank you for reporting back. I am happy to hear you were able to find another way to solve the underlying issue without needing the v4l2loopback-dkms package anymore.
I see you already have backports enabled but probably with low priority (as you should) by default. You can check "man apt" for information how to install that specific version (or use aptitude like I do). That being said, "sudo apt install v4l2loopback-dkms/bookworm-backports" should probably get you the version you need and hopefully it would install fine.
Jaehoon Jeong reacted to laibsch in apt install v4l2loopback-dkms fails