You'll need a Microsoft account to download Minecraft but that's no sweat to do. Choosing between the two versions, Java and ...

Install all Minecraft versions (Bedrock Edition, Java Edition, Education Edition, Classic) on Chromebook (ChromeOS), with or without Linux by following these instructions.

Yes. It is possible to play the Java Edition of Minecraft on a Chromebook. The method to install it is a bit tedious, and it requires a few prerequisites, including a Chromebook sold in 2019 or later.

Using Linux app support to install Minecraft Java Edition The Minecraft Java Edition for Linux will only work on x86 systems. This method will not work for you if you have an ARM-based Chromebook.