Hello there,
First of all, I, too, had to make an account just to thank you for your detailed help @Nyuno. So thank you very much.
However, I think I might have even found an easier way.
When installing the latest JRE 8 from Adoptium (latest JRE 8 for Windows here), you can chose for it to create the JavaSoft (Oracle) registry keys for you, like so:
I also recommend to activate the option above - "Set JAVA_HOME variable".
After installing with those options, it works out of the box, without a manual registry change.
Note: The registry entries also end up in a slightly different location, namely:
"Computer\HKEY_LOCAL_MACHINE\SOFTWARE\JavaSoft\Java Runtime Environment" and the subfolders "1.8" and "8.0.382.5".
Kind Regards,
Merlin