This is a problem not with the operating system, but rather the nvidia DKMS. It can easily be fixed by replacing some lines in the apt sources located here: /etc/apt/sources.list. The line update-security has to be replaced by these two:
<span style="color:#323232;">deb http://deb.debian.org/debian/ bookworm-updates main non-free contrib non-free-firmware
</span><span style="color:#323232;">deb-src http://deb.debian.org/debian/ bookworm-updates main non-free contrib non-free-firmware
</span>
After updating the sources there, simple run sudo apt update and sudo apt upgrade. Then it should finally compile the drivers for your kernel, the extra kernel in the grub menu (if it appeared on your machine) should disappear, and your original kernel (in my case 6.1.0-18-amd64) will have the module in it. So your monitors and stuff should work as they did before.