I have a dog with Pack Puppy level 5 and Pickup Nearby Items turned on.

I placed 64 blocks of copper down to age and then later went back to pick up the aged copper with my dog running around with me. After mining all the copper, I had 26 blocks of oxidized copper instead of 64, so clearly the dog had picked up the rest. However, when I looked in the dog's inventory, there was no copper, only the food I'd put in there earlier.

This bug is confirmed for all fabric version! Thanks for reporting!