I had a similar problem recently after I updated software both on Samsung Gear S3 watch and on my phone Huawei P Smart - Samsung Wearable app. My contacts disappeared from the watch.
To be on the safe side I made a
backup of the watch with the Samsung Wearable app before the update. My plan was that after the update I can restore my watchfaces and screens automatically.
When I finished the process my watch showed only 2 out of 300 of my contacts.
I tried to reset and pair again the watch with the Huawei phone and restored again from backup. Same wrong result.
I tried to pair with my Apple iPhone 5S - I was able to see all of my contacts. Strange.
Then I realised that I did not do the restore from iPhone as I did not make a backup before on it.
So next time I paired the watch with Huawei phone again and SKIPPED restoring configuration and tada: I can see all of my contacts.

However I have to set up again my watchface and screens from the scratch.
So as I can see
backup/restore function of Samsung Wearable is not properly working when restore a backup prepared with a former version of the app. Funny but I was expecting that a backup can be used to migrate my configuration to new versions. So it isn't.
I hope it helped for others having similar problems.
P.S:
check permissions for reading contacts and phone calls when it is requested.