Artifacts are unrelated to the overlap warning. If you want to get rid of the warning, increase the pixel padding in the uv generator.
Those artifacts is what happens when you have open backfaces, since Unity then assumes you are inside geometry and is trying to filter those texels out, to get rid of black texels bleeding in intersecting corners.
You need to not have open backfaces, or failing that, find the material that does and turn on “double sided GI” for that material.
You can try the nuclear option of going to lighting, go down to Lightmap Parameters → Create New, and then on those Lightmap Parameters get Backface Tolerance all the way down to 0.