If you want to store data in a url and the format doesn’t matter (i.e. you’re okay with domain.com/<nonsense text>) then elm-serialize could work. In this case it looks like the url needs to have user readable paths so this wouldn’t work.
Edit: Codecs (generating both the encoder and decoder from a single function) could be an useful approach to handling urls though. I haven’t heard of any attempts to do this. Not sure if that’s because no one has bothered or if people have tried and it didn’t work.