You may potentially need to edit your kernel boot parameters in grub or w/e bootloader you’re using, in case you’re early-loading any CPU microcode. For instance, if you’re loading your Intel microcode via GRUB, you may need to run grub-mkconfig from a chroot (or your old system, if it’s still accessible), or edit your grub.cfg and check the initrd parameter. But if you’re late-loading microcode then you don’t need to worry about it (although late-loading is discouraged and will taint the kernel).
Best to check your distro’s documentation on how to update the initrd / microcode.