Hairy does the “holding” thing with me, but of course I’ve had him since he was 8 weeks old. Dogs’ mouths are their “hands.” Hairy does it out of affection, and I let him. He’s very gentle about it. He does it only to my forearm, when he leans back against the couch in a sitting position. I put my arm up beside his head, and he “holds” my arm for a couple of minutes.
But for a “new” dog, I don’t know how I’d feel about it. Hairy knows I’m the Alpha, and would clearly give his life for me. Your pup barking is a sure sign of bonding with you and your pack.