Moving /home to another disk, which already contains some data, without erasing it

I have the /home folder on the same disk as the root, and I was planning to move it to another SSD drive ("ssd1" in the picture), which is already connected and containing some data:

I checked the devices info with lsblk, and I got:

sda           8:0    0   1,8T  0 disk /media/sda1
nvme1n1     259:0    0   477G  0 disk 
├─nvme1n1p1 259:1    0   512M  0 part /boot/efi
├─nvme1n1p2 259:2    0     1K  0 part 
└─nvme1n1p5 259:3    0 476,4G  0 part /
nvme0n1     259:4    0   1,9T  0 disk 
└─nvme0n1p1 259:5    0   1,9T  0 part /media/ssd1

So, I was planning to do the following:

• Make a backup of the original home folder:

sudo mv /home /home_orig    
sudo mkdir /home

• unmount the partition on the SSD disk from where it is now (/media) and mount it to the new /home folder:

sudo umount /dev/nvme0n1p1
sudo mount /dev/nvme0n1p1 /home

• finally, make a backup of the original fstab file, and modify it this way:

sudo cp /etc/fstab /etc/fstab_orig
sudo nano /etc/fstab
UUID=<>    /home    ext4    defaults   0  2

Is this the correct procedure? I checked this link and this other answer, but the situation seems slightly different than mine...mostly, I'm worried about potentially deleting the data already present on ssd1.