At the moment, I can read .aeon files, but I cannot write them (in contrast to Aeon Timeline 2 .aeonzip files, which I can synchronize with yWriter, for example).
For details, see this discussion thread:
Currently, in aeon3obsidian.py is a lot of code that is reused from Aeon 3 to yWriter export. This is why the export is limited to a yWriter-like data structure. The development potential therefore lies in exporting all user-defined structural elements and relationships as far as possible.
Another problem, which would also apply to an Aeon 3 internal synchroniser, is that Aeon Timeline has a fixed data structure, whereas Obsidian only has a set of interlinked files with free-form content. I imagine that reconstructing a hierarchy backwards from this would be complicated and error-prone.