That's okay... Let me try to explain what I see from all that output, and tell the story it tell's...
*** The only kernel that is currently there in the /boot folder to actually boot from is kernel 5.15.0-87-generic. ***
That is odd, because package-wise it says that these kernels are installed:
Code:
linux-image-5.13.0-37-generic
linux-image-5.13.0-39-generic
linux-image-5.15.0-87-generic
So the kernels for -39 and -37 didn't completely install correctly (no initramfs images present in /boot). It looks like the problems started with -37 back in 20.04... Either that, or it started to remove them , then when that failed, didn't roll anything back. It shows -87 as the current running kernel...
Your updates are trying to install kernel versions 5.15.0-88-generic and 6.2.0-36-generic... Those are the current kernels for 22.04 in the generic and generic-hwe series.
This starts a change of events... When Ubuntu installs a new kernel, it leaves 2 previous kernels, and tries to remove the older kernels than those.
It sees kernel 5.15.0-87 as an installed package, is booted from that as the latest kernel.
It's trying to remove the oldest kernels, so that after the install of the 2 new kernels that there will be the newest, and 2 older kernels (6.2.0-36, 5.15.0-88, 5.15.0-87). That would be the right things to do.
But it can't, because it cannot remove those because there were some problems. It cannot resolve those problems on it's own.
Did you follow that logic?
Let's try to check if they are even available anymore through his apt system. Becaseu they were 20.04 kernels, and he is now 22.04...
Code:
apt list linux-*-5.13.0-37-generic
I see those in my 22.04 results...
Code:
sudo update
sudo apt install --reinstall openssl
sudo apt install --reinstall linux-modules-extra-5.13.0-37-generic linux-modules-extra-5.13.0-37-generic linux-headers-5.13.0-37-generic linux-image-5.13.0-37-generic
sudo apt install --reinstall linux-modules-extra-5.13.0-39-generic linux-modules-extra-5.13.0-39-generic linux-headers-5.13.0-39-generic linux-image-5.13.0-39-generic
The run your updates to see if they get removed successfully.