I have seen this other Super User question, but it does not really answer my question.
Running blkid can list both partitions and partition labels on a disk:
ubuntu@ubuntu:~$ sudo lsblk -o NAME,FSTYPE,SIZE,MOUNTPOINT,LABEL
...
sda 111.8G
├─sda1 vfat 350M SYSTEM
├─sda2 ntfs 50G Windows
├─sda3 ntfs 1.5G Recovery
├─sda4 1K
├─sda5 ext4 20G ubuntu
├─sda6 ntfs 30G extra
└─sda7 swap 9.9G [SWAP]
As the linked post notes (also found with info found here), I can use sfdisk to backup the partition table on this disk, /dev/sda:
sudo sfdisk -d /dev/sda > sda.partition.table.txt
Which could then be used to restore the partition table with:
sudo sfdisk /dev/sda < sda.partition.table.txt
However, printing this file, shows that there are no partition labels (in my example: SYSTEM, Windows, Recovery, ubuntu, extra):
$ cat sda.ljuttpx220.partition.table.txt
label: dos
label-id: 0x5e4a12da
device: /dev/sda
unit: sectors
sector-size: 512
/dev/sda1 : start= 2048, size= 716800, type=ef, bootable
/dev/sda2 : start= 718848, size= 104857600, type=7
/dev/sda3 : start= 231292928, size= 3145728, type=27
/dev/sda4 : start= 105578494, size= 125714434, type=5
/dev/sda5 : start= 105578496, size= 41943040, type=83
/dev/sda6 : start= 147523584, size= 62914560, type=7
/dev/sda7 : start= 210440192, size= 20852736, type=82
So, is there a command or a procedure that would allow me to backup BOTH the partitions AND their labels in one go?