ahrefs I have a question on the link index.

When searching site: domain, you can see that the 2.0 web blog is indexed. But why can't I get a backlink on ahrefs?
And can I continue to work on the link in this state?

Ahrefs don't have the same backlink analysis processes as Google does. They do the best they can with the resources they have, but Google is a mega empire while Ahrefs is an moderately big company hundreds of times weaker in terms of indexing power.

You can continue without issues, Google is the only thing that really matters, Ahrefs is just an orientation tool that serves to get a big picture of something.