I'm familiar with applets, but hadn't heard of Java Web Start. Could Java Web Start interact with the DOM?
It's been used in place of applets a lot, but mostly because you could provide a complex application that opened in a new window with a click (assuming you dealt with the CA shenanigans).
It couldn't interact with DOM unless it accessed a browser over something like COM.
It's based on CheerpJ, a JVM that runs in the browser (using JS and Wasm).