Note that the Backup utility if Sailfish OS saves only so-called local contacts. It does not save the contacts synhcronised to/from a cloud service (e.g. gmail) as that would be unnecessary.
The backup data is in file
sailfish_backup_201*.tar in the SD card or on a cloud service like Dropbox.
In the following example we assume that this file is located in the SD card. You need the Terminal app (which is installed by enabling the Developer mode) or an SSH connection to the phone.
Do this to extract the contacts from it:
## You will see the card ID now - it has the notation xxxx-xxxx.
## You may have many of them - take the latest (date in the file name) and use it in the tar command below.
tar -xvC tmp/ -f sailfish_backup_<append-here-the-name-of-the-latest>
ls -al tmp/People/data/
### Check the size of file all.vcf . If it is > 0 kB in size, then it has some content.
The next thing, given that file
all.vcf has some content, is to import the contacts to People app. To do this, visit "Settings > Apps > People" and tap "From contact file". Tap "all.vcf" and you are done.