What browser are you using? I'm happy that it works for you 😃 I will check, what other browsers are working. With Chrome it does not work for me.
This time I used serialization for saving the data, but in the past game jams I always used playerprefs. This time serialization was easier, because I save arrays of BigIntegers. So yes, you can use serialization with webGL, but it seems, that it is a bit buggy.