Earlier quoted context omitted.
Here you go: https://chrome.google.com/webstore/detail/cheerpj-applet-run... CheerpJ does exactly that: it ships a full JVM implementation (including Swing/AWT, Threads, ...) that runs in JS/Wasm inside your browser. The Applet Runner extension detects applets in the page and runs them through CheerpJ. The example that you list seems to work.
I know about the extensions, it's exactly how I was able to run that specific applet, but that's a high friction experience for the user. If the applet does not run it's very unlikely I will install an extension (or search for a Firefox alternative) unless I'm very motivated. I'm thinking more like a line or two you can add to your pages hosting applets, and it would enable any modern browser to use it. Minimal frict…
See "Converting an applet"