Initially I thought it was a bug. It didn't make sense to me, that 11.31% increase in ATK was performing better than a trait that is supposed to boost Melee Power by 18%. So I did some more testing, using a bunch of Shooter builds, since I had more traits and higher end Shooter parts than Melee ones.

Sadly, I don't have the exact parts list for each of these builds, since they change frequently, but the important thing was typing was kept the same throughout, being T type or neutral type, both identical vs Sana's T type Dianthus. The tests also include all the important information needed, namely ATK values and trait bonuses. I even did a test with no word tags at the suggestion of a member of the discord, to see if that caused something to break.

Test 0:

12529 Shot ATK, using XB1 Torso

2200 to 2400 range per beam

This was the baseline test. I took my Test 1 build (more on that in just a second), replaced all the trait parts with parts with similar Shot ATK, and used that as the baseline. Hence, Test 0. The "range per beam" means that each of the four beams from the Crossbone X1 (henceforth known as XB1) Torso's Beam Gun EX Skill did between 2200 and 2400 damage, ie, the damage range was between 2200 and 2400.

Test 1:

12497 Shot ATK, Using XB1 Torso, +62% EX Skill Power

3600 to 3800 range per beam

So here we have the highest part trait boost I was able achieve at the time for Shooters, at +62%. We see a significant boost in damage, and more importantly, the average of the Baseline, 2300, when multiplied by 1.62 (+62%) gives us 3726, with the average of our Test 1 being ~3700. So this initial test, at least, seems to confirm that the traits boost your final damage by the amount shown in the trait description.

Next, let's look at raw Shot ATK increases, without part trait boosts.

Test 2:

16048 Shot ATK, Using XB1 Torso, no tags, no boosts

3200 to 3500 range per beam

Test 3:

16985 Shot ATK, Using XB1 Torso, Ace Exclusive, no boosts

3600 to 3800 range per beam

Test 3 is the interesting one here. We see that at 16985 Shot ATK, the damage increase is the same as in Test 1. But how much more Shot ATK does Test 3 have compared to Test 0? Well, I'll save you the trouble and tell you. It's a ~35.56% increase in Shot ATK. That means a ~35.56% increase in raw Shot ATK that you can see on your stats screen is the same as a collection of traits that boost your EX Skill Power or Shooting Power by 62%.