You’re not doing anything wrong. This is a giant gap left in the (initial) implementation of ES modules in browsers. There’s work in progress to make it (a little) easier with import maps, but that’s only available on Chrome, behind a flag, and still requires you to create such a map.
You should be able to use a server like esmoduleserve to rewrite non-precise imports to precise ones on the fly, and load a ProseMirror-based app that way. I haven’t tried yet with ProseMirror, but that’s how I’m doing development on CodeMirror 6 now, which has a very similar module structure.