If you click through to the link from your quoted sentence, the 2023 paper "provided a new recipe for how to densely pack spheres in all arbitrarily high dimens

If you click through to the link from your quoted sentence, the 2023 paper "provided a new recipe for how to densely pack spheres in all arbitrarily high dimensions", and from the description the new paper also seems to address the same question. This is different from asking about the best-known specific packing in n dimensions when n = 7, 10, 19, or whatever. In a few of the specific low dimensional cases, my impression is that the best currently known packing is not regular, and I don't see any evidence that this has changed. Perhaps this new method will give people a way to beat those records, or perhaps not.