Hi,
I’ll start by leaving this here.
On to your issue…
Lets see;
First check mhwd-kernel which is how it should be handled, then check the package manager just in case.
mhwd-kernel -li
pacman -Qs 'linux5|linux6'
You can then remove the 6.1 if it is there:
sudo mhwd-kernel -r linux61
Or, if for some reason there are packages installed outside of mhwd
sudo pacman -Rns linux61 linux61-headers
When thats done you can double check a few file locations:
ls /lib/modules
ls /boot
Note: I always find its good practice to keep 2 kernels installed - 1 LTS thats known to work plus another one, usually newer and/or experimental. If you want to install another kernel you can like:
sudo mhwd-kernel -i linux515
When you are satisfied you have the kernel(s) you want installed and everything is clean, then you can update grub:
sudo update-grub
Give it a reboot and check I guess.
PS - Grub should allow you to select kernels at boot. If it is invisible you can try hitting Esc to try and bring it up.