My camp-dog does not eat any food except if it is placed in front of it on the ground?

Should they not share the food with the group like the others?

yep!
And the option to share food is enabled. I only noticed when "Rocky" was down to 154 and then tried to give him food by dropping it into its inventory, could not.
Then I had the idea to drop some cooked meat to the ground in front of it, though we do have a food-storage everyone uses, and it worked.

that is odd.
as they supposed to share if in same squad.
If the issue persists then i suggest you file a bug report on the main forum ( Or Steam ) and include your zipped up affected save folder.

I got one reply, saying that the food needs to be in the backback and not the normal inventory, dogs cannot access food supplies and cannot enter buildings, though I read from others only to a certain size and my dog totally enters buildings all the time, the moon has to full and a bright star needs to be on the firmament for dogs to share food with the squad.

https://www.lofigames.com/phpBB3/viewtopic.php?f=9&t=14438

But at least someone did :)