This is my current setup, I need to add a string of 3 more lights to the first switch where the power arrives at.
SMH, these clickbait sites and their stolen and re-stolen diagrams. First let's get some colored tape and mark our wires for their actual function.
That's more like it. One messenger or the other is energized, depending on the switch position. So they are functionally alike.
As you can see, for a light to work, you need switched-hot (red) and neutral (white). Are both present in switch box 1? Nope. Switch box 2? Nope. Only at the lamp box do those exist.
So if you want these lights to work with the existing switches, you need to tap off the lamp box.
If you want a separate string on a separate switch, you can do that in box 1. You would use a dual 3-way switch, which is meant to fit in a single box, and gives you two 3-way swiches. For the new string, you would just use it as a 1-way switch by not using one of the brass screws.