I do not see any repositories listed that are Proposed Repos; but I do note that you are being advertised to use Ubuntu Pro...
It looks like the Nvidia 340 driver is unsupported on later kernels. You may need to use a kernel that still supports it.
Which explains:
You also said that you can boot 5.4...
So you may need to Lock In the 5.4 kernel to make sure that you stay on that kernel and always boot into it. Using the Recovery Menu Prompt:
Remove the 5.15 kernel:
sudo apt remove linux-headers-5.15.0-84-generic linux-modules-5.15.0-84-generic linux-modules-extra-5.15.0-84-generic linux-image-5.15.0-84-generic
Reinstall the Nvidia 340 driver:
sudo apt install nvidia-340
You do not need to use DKMS since you are locking in the kernel and not allowing it to upgrade.