I think it's just the base damage. At least, I've noticed it changes the stat once I actually equip a weapon that has the armor based damage modifier perk (whatever that one's called).
I really wish there was better stat info for the gear in this game. I don't want to have to do the math to figure out DPS every time I think about swapping out a weapon, especially if it changes the stats based on perks and skills when you equip it. On XBox, I can't even install that nifty inventory mod someone made for PC. Bummer.

Yes, it does, for most of the skills. If you really want to know how damage works in Starfield here's a good YouTube video describing how it actually works: https://youtu.be/Na-byGrNFcU?si=eL43ifhHzZUVyqWc

I'm pretty sure it does because whenever I put points in some of my combat skills I definitely saw the numbers in my inventory increase as well.

However, I do want to add that I use the inventory mod and I have used it since I started so I'm not sure if it's the mod or if the vanilla game does this as well.