Deploying a Java game on Steam

Hello,
Forgive me for asking, but I fail to find documentation related to my problem.
I’m a hobbyist game developer preparing my first release on Steam. My game has only one dependency: java JRE. Surely there is other games on the platform with such a common dependency. However I do not understand what is the preferred way to handle this dependency as of now:

  • It seems that packaging the JRE into my binaries is frowned upon by Oracle and not really a recommended practice.
  • It seems that install script will only help me on Windows, not Linux or Mac.
  • It seems that any solution that I’ve found on the web mentioning shared package may be deprecated ?

Would you please advise me on the best way to handle a JRE dependency?
Thanks a lot!