Thanks for the answer @GrandSchtroumpf. On Linux, I only see one executable "Superpowers" which launches the server manager.
However, I've found out that you can run Chrome (or, in my case, Chromium) in "app mode" just doing:
$ chromium-browser --app=http://localhost:4237
This works more or less like a proper app, although you still get some window decoration, and right-clicking shows the usual Chrome(ium) contextual menu. Another option is to use the kiosk mode, like:
$ chromium-browser --kiosk http://localhost:4237
This runs always fullscreen (it's in fact, intended to be used in by actual digital kiosks). However, it seems that it does not work if you have the browser already open (which is likely), so in that case you can trick it by setting a different user directory:
$ chromium-browser --user-data-dir=<some directory> --kiosk http://localhost:4237
I think I'll stick to the --app option anyway.