To fix your Btrfs + LUKS layout that isn't booting, follow these steps exactly:

Use a Gentoo/Ubuntu live ISO to boot into a live environment.

(Adjust device if needed)

cryptsetup luksOpen /dev/sda3 cryptroot

Your layout shows:

Mount the root subvolume first:

mount -o subvol=@ /dev/mapper/cryptroot /mnt

Mount the other subvolumes:

mkdir -p /mnt/{boot,home,var/log}
mount -o subvol=@home /dev/mapper/cryptroot /mnt/home
mount -o subvol=@log /dev/mapper/cryptroot /mnt/var/log

If you have EFI:

mount /dev/sda1 /mnt/boot   # adjust if needed

mount --types proc /proc /mnt/proc
mount --rbind /sys /mnt/sys
mount --make-rslave /mnt/sys
mount --rbind /dev /mnt/dev
mount --make-rslave /mnt/dev

chroot /mnt /bin/bash
source /etc/profile

Ensure it uses subvolumes: Example:

/dev/mapper/cryptroot  /        btrfs  subvol=@,defaults  0 0
/dev/mapper/cryptroot  /home    btrfs  subvol=@home       0 0

Ensure it exists:

cryptroot UUID=<UUID-of-sda3> none luks

Get the UUID of `/dev/sda3`:

blkid /dev/sda3