My blog or single-page website does not appear in Obsidian.

Micro.publish does not automatically update the list of blogs and single-page websites. This approach is intentional to reduce the number of network requests.

To refresh the list manually, open Obsidian Settings, go to Micro.publish, and click the refresh button next to the list of blogs.

I am unable to post anything after adding a custom domain to my blog.

In Micro.blog, your blog ID is equivalent to your blog domain. When you add a custom domain to your blog, it is necessary to update the blog list in Obsidian. To do this manually, open Obsidian Settings, proceed to Micro.publish, and click the refresh button next to the list of blogs.

To edit or update blog posts previously published via Micro.publish, it is also necessary to update the URL references in those notes. Adjust the URL in the Properties or the YAML front matter to reflect the new domain.