The issue was in the sync byte, which I got from synchronous transfer and there it is different.
Now, I have other issue. When reading the contents from AT3 (in the command structures), I get following command:
[57][02][00][00] - I cannot see such command in the AT3 documentation, I suppose it is "set default sector 0" command, which I sent there while programming, but the byte order does not follow the documentation.
Similarily, I have:
[57][03][BD][00] - which is probably supposed to be "End of sector" (byte order also does not follow documentation), but I dont understand what does 0xBD stands for.