Hello again,
two weeks later I was successful to finally got my HP Pavilion laptop working again! 
Feedback desired: 
Iâm still not entirely sure what the crucial step was, but Iâd like to share my approach with you in case anyone else needs help with an NVIDIA/CachyOS black screen.
The laptop now boots flawless with the two main CachyOS kernel options. But now Iâm wondering whether that was the right way to do so and a wise decision. I managed to do it on my own and learned a lot in the process, but ultimately the end I need a system that works. I donât want to run into problems again with the next update. I would appreciate any comments and objections.
The Context and the core problem:
The initial failure was caused by a broken(?) kernel update on my CachyOS installation (running an NVIDIA GTX 960M and Intel Iris 530). This resulted in a black screen after restart, preventing the system from booting.
My recovery process started by booting into a CachyOS Live USB stick and gaining access to the installed system using cachy-chroot.
Crucial Sequence: After the update failed and the black screen appeared, my first attempt to fix it was to uninstall all NVIDIA packages and install them again. While this seemed logical, it possibly exacerbated the problem: the system continuously did not start and continuou with black screens even though the Intel iGPU was present. The ultimate fix was to restore the graphics drivers using the more stable DKMS method.
IMPORTANT DISCLAIMER: USE AT YOUR OWN RISK 
I am a ânoobâ, simply trying to recover my system, and my approach is not the officially recommended one. Please use this information at your own risk.
Repair Steps (Executed within cachy-chroot):
- First, I removed all installed NVIDIA packages and just wanted to use the Intel Iris 530 GPU alone, believing this would solve the conflict. It turned out that rebooting was still not possible.
sudo pacman -Rns $(pacman -Qq | grep nvidia)
- Next, I attempted automatic configuration and expected to automatically reinstall the drivers. Both GPUs, GTX 960M and Intel Iris 530 were shown as already installed. That was confusing.
sudo chwd -a
- I thought that the kernel needs to be initialized/rebuild again. But I was finding a critical module failure by attempting to rebuild the Initial Ramdisk (Initramfs).
sudo mkinitcpio -P
- To resolve the module failure, removed the CachyOS Nvidia drivers and installed the NVIDIA-DKMS package, as I had found evidence that the asynchronous NVIDIA and Arch-Linux kernel cycle could cause problems spontaneously after an Nvidia driver update. (Is that true?) I also explicitly removed the static Linux-Cachyos-Nvidia package to hope that there were no remaining conflicts.
sudo pacman -Rns linux-cachyos-nvidia
- Install the DKMS drivers, kernel, and headers to restore the systemâs graphics drivers.
sudo pacman -Syu --needed linux-cachyos linux-cachyos-headers nvidia-dkms nvidia-settings
- Final successful integration of the newly built DKMS modules into the Initramfs.
sudo mkinitcpio -P
- Update the systemd-boot bootloader configuration
sudo bootctl install
- I then exited the cachy-chroot session and finally performed a successful reboot:
exit
sudo reboot
- After reboot, the system worked but suddenly presented three boot options.
- Linux
- CachyOS-Linux
- CachyOS-Linux(LTS)
I removed the âLinuxâ kernel entry that had been added:
sudo pacman -Rns linux linux-headers
And updated the boot section again:
sudo bootctl install