Never heard about The Story Graph before, but it looked cool so I created an account to check it out. I could not find any way to create custom integrations (or make any integration at all).

One option would be to pull your data from ABS via its API and then use JavaScript to navigate The Story Graph’s website to “manually” update your progress.

Edit: If you want to work with Python, someone has created a library to work against their website as if it was an API: https://github.com/ym496/storygraph-api/tree/main
It uses an HTML parser to map the response from the website.

Would be cool, as I use both these and currently just update daily.