My attributes show 8-9 damage but my swords are well above that in terms of damage they do.

Or is that the amount of damage bonus I'm receiving from mutagens/trophies?

Do you have your sword out in your hand when checking?

Otherwise I believe it just shows your fist fighting damage.

Or maybe it's there to show the bonus damage on top of the sword.

Notice the wraith trophy. It doesn't add to your sword damage, but it gets shown in the attributes section when you're unarmed. That's the damage on top of the sword.

Similarly, with Addan Deith at 60ish damage, after downing some potions and using a whetstone, unsheathing the Addan Deith then checking the stats screen showed damage somewhere around 134-180.

you have to meditate to see the attributes so Geralt sheathes his sword anyway...

Not if you hit the "C" key.