Suppose the dwarf has a shield in his left hand, and he fails his dodge and shield-block attempts, but the attack hits the left arm or left hand. In that case, the shield is functioning as armor. This is just a guess...
It doesn't appear to be the case, since if the hit disables the hand, they drop the shield (in contrast, a gauntlet isn't lost unless physically removed,) similar to if they're using a scepter or whatever in their main-hand and
that hand gets disabled. Basically it's not armor in the traditional sense that will tank a hit to your left hand if it gets hit - you need a gauntlet there for that.
As far as I can tell - there's just about no limit to how many things and how much weight you can carry in one hand. Take - or example - using the carpentry bench in adventurer mode. You'll end up with 4 beds in one hand. Likewise, you can fill a lead cage with dragon corpses and walk around (very slowly).
[UPSTEP] - "Length of gloves or footwear, counted in [LIMB] body parts towards the torso. A value of 1 lets gloves cover the lower arms, a value of 2 stretches a boot all the way over the upper leg and so on. Regardless of the value, none of these items can ever extend to cover the upper or lower body. Shields also have this token, but it only seems to affect weight. "
According to the wiki also seems a bit of a mystery.
Theory: Those tags on a shield determine how much of the arm they cover while in use, influencing attacks on that arm: That is, if a dwarf has a shield on their left hand, then attacks to their left arm will have a higher "difficulty" vs an attack to the weapon arm or legs, with that chance to block being used to "cover" for the exposed limbs alongside other armor.
Could probably test that in the arena and just see how easy it is to target the weapon arm and legs vs the shield arm.