I read an article interviewing a Priest that consulted on “The Passion” with regard to this. Mel did a lot of research to try to determine the historical accuracy. What he found was that it was done both ways. It would be done through the wrist to support the body weight for some people. For others, it was through the palm, and the hands were secured with ropes.
The Shroud appears to favor the wrist theory, but other things favor the palms. For example, when Jesus confronts Thomas, we see the word hands - but this is muddied because the translation could also probably have been rendered “wrists.”
I believe that Stigmata accounts are in the palms, so this was a factor. Finally, any artwork we have tends to show the nails in the palms. One could surmise that there is a reason for that.
In the end, Mel decided there was not overwhelming evidence either way, and since most people tend to picture the nails through the palms, and certainly our crucifixes and artwork do, then it would be a more familiar way of presenting the crucifixion.
So, I think the answer is we will probably never know for sure until we meet Jesus for ourselves. In the end, it’s not important. Either way, what an incredible sacrifice He made!