CodeBlock+ is a Confluence macro that runs on Atlassian Forge.
The macro's own settings (code, title, language and display options), which Confluence hands to the macro when a page opens. It also reads the license state Confluence provides.
Nothing outside the page. The code and settings are saved in the macro on the page, the same way Confluence stores any macro's settings. The app has no database, no key-value storage and no logs of its own.
It doesn't call any server outside Atlassian, load fonts or scripts from a CDN, or read other pages, spaces or users. It doesn't collect analytics. The manifest declares no scopes and no external hosts, so Forge would block such calls anyway.
Uninstalling the app leaves the macro settings on your pages, because they're page content. Reinstalling shows the blocks again.