First things first. You updated the kernel, and graphics failed after the update. Two things come to mind. Exactly what packages did you install? On a working system, on slackware 15, with the latest kernel this is what I see.
Code:
ls -l /var/lib/pkgtools/packages | grep kernel
-rw-r--r-- 1 root root 105K Jan 25 09:08 kernel-firmware-20220124_eb8ea1b-noarch-1
-rw-r--r-- 1 root root 979 Mar 9 09:48 kernel-generic-5.15.27-x86_64-1
-rw-r--r-- 1 root root 31K Mar 9 09:48 kernel-headers-5.15.27-x86-1
-rw-r--r-- 1 root root 975 Mar 9 09:48 kernel-huge-5.15.27-x86_64-1
-rw-r--r-- 1 root root 323K Mar 9 09:48 kernel-modules-5.15.27-x86_64-1
-rw-r--r-- 1 root root 4.8M Mar 9 09:52 kernel-source-5.15.27-noarch-1
You do not need both huge and generic kernels installed, that is a default and is fine if you have both. You must have the modules package that matches the kernel you have installed, if not, no graphics and most other periferals won't work. Headers you need if you are compiling software. You don[t need the course unless you want to recompile your kernel. The latest firmware is recommended, however, older firmware will still work if ir supported your hardware and you have not put anything in new not supported by the firmware.
Once install, if you are using the generic kernel, you have to build a new initrd file. Did you do that?
In your /boot/efi/EFI/Slackware directory, did you copy the new kernel and initrd file in place? How did you do that?
What boot loader are you using? Grub or elilo?
You have been messing with the UEFI settings. Secure boot should be turned off, and fast boot also.
You have not stated if this is a dual boot with windoze? Is it?
Have you looked in the T460 documantation to find the hot key for selecting the nvram boot options? What is the next boot set to? Is it Slackware, or something else?
You need to post useful information for us to guide you further.