Yes, I had explicitly selected grub during the installation over half a year ago, as I never had any problems with it in my previous Linuxes.
I’ve found the LTS kernel not listed in /boot/grub/grub.cfg, so i tried your command sudo grub-mkconfig -o /boot/grub/grub.cfg.
That was the mistake! My sudo grub-mkconfig wasn’t enough due to the failing path to grub.cfg.
I think you are missing the point. You can use grub or you can use systemd-boot. If you re-install the system with grub you can add the lts kernel on the install. If you are installing the lts kernel afterwords it depends on how you are installing it. There is the package akm which is a kernel manager that can install the lts kernel and headers. If you install the lts with pacman you have to install the headers as well. Then you would need to run the grub update command to have it in the boot menu.