How can I format an inline code in Confluence like this? I mean, not a separate code block, but just inline classname, for example.
To insert inline monospace font in Confluence, surround the text in double curly-braces.
This is an {{example}}.
If you're using Confluence 4.x or higher, you can also just select the "Preformatted" option from the paragraph style menu. Please note that will apply to the entire line.
Full reference here.