The new system is still being developed and tested, it's not ready for use yet, however there are manually-created mapping versions pinned in the modder-support-116 channel of the Forge Discord
I recommend getting Java 8 HotSpot from https://adoptopenjdk.net
Your issue appears to be that your JRE is missing a certificate to authenticate the Forge server so the installer won't accept the file from it, the above website provides OpenJDK versions that are known to have the correct certificate