There are three simple ways to set JAVA_HOME in Windows. This tutorial shows you how to do it manually, from the command line and through the installer.

All software fully updated. On Bootcamp is Windows 10, 64bit version, fully updated as well. - I need to install Java on this Windows partition, but fail to do so: ...

If you don't yet have it setup, I've written a complete guide on how to setup and install WSL2 on Windows 10 and 11 you should check out first.