Jacob and Heli were half-brothers as they had the same mother but different fathers. Heli married but died before he had any offspring so Jacob took Heli's wife as per Deuteronomy 25:5-6.
The second-century historian Julius Africanus, a native of Israel, records information given by Christ’s remaining family in his day.
This was explained in the (Eusebius, Ecclesiastical History 1:6:7). I will post the exact section for you.
https://greekdoc.com/DOCUMENTS/eusebius/book-1.html#chapter-7Eusebius of Caesarea (c. AD 260/265 – 30 May AD 339)
So you arrived at a conclusion that they are 1/2 brothers because some guy +265 years after jesus told you they were related not by the bible itself?
What you have is a very elaborate explanation of a very obvious contradiction and you are basing it on some guy's opinion? How did this Eusebius guy conclude that Heli and Jacob were 1/2 brothers?
What source is he drawing these findings and presenting them as if they were facts?
Remember I am not saying that your explanation isn't possible but the more I dig the more it sounds like mental gymnastics. I am trying to ask these questions as a detective or a forensics would leaving no stone unturned, I want to make sure its not built on assumptions. So far you just copy pasted someone else's opinion and presented your TED Talk as facts. Talk about irony.