Firefox
Drop-in replacementFreePreinstalled on most Linux systems. Open scratch.mit.edu and the full editor is there.
Your files: Uploads and saves .sb3 project files exactly as the Windows app does.
Verdict: Partly
Partly. The Scratch website works fully in any browser on Linux, but the downloadable Scratch app is offered for Windows, Mac, ChromeOS and Android only, with no Linux version.
Almost everyone uses Scratch at scratch.mit.edu in a browser, and that is exactly what a child on Linux does. Log in with the same account used at school or at home on Windows, and every project is already there. Making, editing, sharing and remixing all work the same.
The offline Scratch App is the part that does not come across. Scratch lists it for Windows 10 and later, macOS, ChromeOS and Android, and Linux is not on that list. If a school insists on the offline app specifically, that is a real gap worth raising with the teacher, because the browser version is the same editor.
Projects live in the Scratch account rather than on the hard drive, so there is usually nothing to migrate. If your child has saved .sb3 files locally, those upload into the website editor without changes.
The one requirement is a reasonably current browser, which Firefox or Chromium on any mainstream Linux system satisfies.
Preinstalled on most Linux systems. Open scratch.mit.edu and the full editor is there.
Your files: Uploads and saves .sb3 project files exactly as the Windows app does.
Use this if a site or school tool is fussy about browsers. Same Scratch editor.
Your files: Uploads and saves .sb3 project files.
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