In this case there is only one Linux filesystem - it is fair to say this is the important partition with relation to Manjaro.
Proceed to create two temporary mount points in the live user home
mkdir ~/root
mkdir ~/usb
Mount the partition nvme0n1p8 temporarily
sudo mount /dev/nvme0n1p8 ~/root
Attach your external disk and repeat above command to identify the external disk
When you have identified the external disk - mount the disk’s storage partition e.g. /dev/sdy1 - ensure there is enough space to hold your uncompressed data.
sudo mount /dev/sdy1 ~/usb
Create a folder to hold your backup the**$(date +"%Y%m%d%H%M")
** will be a timestamp
Create a variable with a timestamp
timestamp=$(date +"%Y%m%d%H%M")
Create the backup folder
mkdir ~/usb/backup-$timestamp
Use rsync -a to backup /etc to the storage device (files readable only by root will only be copied if run as root).
The -a flag stands for “archive” and syncs recursively and preserves symbolic links, special and device files, modification times, group, owner, and permissions.
rsync -a ~/root/etc ~/usb/backup-$timestamp
List the content of the root/home to identify the username e.g. fido
$ ls ~/root/home
fido
Use rsync to backup the home folder e.g. fido
rsync -a ~/root/fido ~/usb/backup-$timestamp
Verify the content of your backup - and when satisfied - do what you gotta do.