Motivation for this change

Source is always better I guess, supports more architectures and we can patch things if needed.
Depends on #82349

Screenshot of WebStorm running with source-built jetbrains-jdk:

Currently IntelliJ IDEs show this warning:
Early Access Java versions may cause compatibility issues. Use a stable release version.
This check is located here: https://github.com/JetBrains/intellij-community/blob/master/platform/platform-impl/src/com/intellij/ide/SystemHealthMonitor.java#L63

Things done

• Tested using sandboxing (nix.useSandbox on NixOS, or option sandbox in nix.conf on non-NixOS linux)
• Built on platform(s)
  • NixOS
  • macOS
  • other Linux distributions
• Tested via one or more NixOS test(s) if existing and applicable for the change (look inside nixos/tests)
• Tested compilation of all pkgs that depend on this change using nix-shell -p nixpkgs-review --run "nixpkgs-review wip"
• Tested execution of all binary files (usually in ./result/bin/)
• Determined the impact on package closure size (by running nix path-info -S before and after)
• Ensured that relevant documentation is up to date
• Fits CONTRIBUTING.md.