This one is only an error from the package Package kit, where someone suggest, to simple remove it with pacman -Rs Packagekit because it caused more problems at past and is not really needed.
That digit [12] at inxi was indeed, because you been in a chroot enviroment.
I think pretty all distros are the same, if something breaks, you are with all in trouble.
I wouldn’t say “This or that one is not for you” as far you look for solutions and got a little understanding.
For a reinstall, i did learn, that a easy way is to have /home on a separate partition, so if you install the system new, you can simple keep it, just mount it at the new installation as home and use the same user and password, and it will work again.
And well, Ok, my bad, mounting nvme0n1 is useless, you can’t mount a disk when it contains partitions. I did read that wrong.
That error about error: cannot find a GRUB drive for /dev/sda1 is probatly only because there is no grub installed, seems that is not a problem.
But i am still not out of Ideas.
You can look at your pacman log file, after you chroot, at /mnt/var/log/pacman.log
maybe with nano /var/log/pacman.log or from the live iso with an editor.
It can be some big, so you may have to scroll down far.
Maybe you can see there some errors during the update.
And may install another Kernel ie, 6.1, what is still LTS with pacman -S linux61 and see if you can boot that.
i would also try a mkinitcpio -P and install-grub this time.
The package should now work, since pacman showed, it is installed.
There is another error, ERROR: mkdir /var/lock/dmraid
what points with a problem with an raid system, but maybe better ignore it right now too, or do you have / had a raid installation?
There is a topic about it, but i dont wanna suggest now you should delete anything.