To reinstall the bootloader in my situation, I just had to do the following steps:
apt install --reinstall linux-image-generic linux-headers-generic
update-initramfs -c -k all
sudo bootctl --path=/boot/efi install
And audio works! 🙂 Only two speakers work, though, as the onboard sound only has a single line out port compared to the old system. I’ll need to go through Logitech’s documentation again later to see if there’s a way to get the others working without dedicated ports for them.