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.

Everything you need to know to install and play Snapshots in Minecraft Java Edition.

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.