There is no such discussion, at least not among historians. At the same time early crossbows were used in China Greeks were using crossbows, too. There have been many parallel inventions over the course of history and this appears to be one of them.
It is a fun misconception in general. As though two or more people separated by distance couldn’t have the same idea. Only one person in one specific place would figure out pointy things are good for stabbing and have the thought to make pointy things to optimize stabbing.
Since physics more or less stays the same, most machines and tools for a given purpose share similarities in fundamental design. The most efficient mechanism or simplest or most reliable etc. will tend to be selected and that will tend to stay the same.
There are often differences in technology relating to cultural reasons or the materials and infrastructure available or differences in specifics of use. Rice farmers and wheat farmers will have some similar tools but the differences between specifics of farming rice and wheat will shape the tools of course.
But this is part of why the whole preoccupation with who “invented it” or “thought it up” is often silly. If Newton hadn’t conceptualize dls gravity someone else would have. People often say in a moment- “you know what would be great is if they made a <blank> that did <blank>!” Then someone says: “they have that. It’s called a <blank>” sometimes people laugh after at the oversight etc. but that’s an example of someone independently coming to the same idea as someone else because they faced a situation of need and came to same conclusion as the “inventor” did in their moment of need that the solution looked a certain way.
Since physics more or less stays the same, most machines and tools for a given purpose share similarities in fundamental design. The most efficient mechanism or simplest or most reliable etc. will tend to be selected and that will tend to stay the same.
There are often differences in technology relating to cultural reasons or the materials and infrastructure available or differences in specifics of use. Rice farmers and wheat farmers will have some similar tools but the differences between specifics of farming rice and wheat will shape the tools of course.