I believe you want:
(or one of the alternatives mentioned there, OR this latest package):
[EDIT: It used to be called Websocket.jl when I originally wrote this post, was renamed, see link at the bottom.]
I noticed the latter package registered a few days ago, but now when looking into it, it seemed to have years of development, and I was confusingly looking at the former package…
I do not know too much about these packages, or the standardized API, but I believe it’s exactly what you’re looking for. You would runs some JavaScript code in the web browser to access the Julia websocket. In general you can compile Julia code to JavaScript too, with JSExpr.jl, but I’m not sure if it helps with this, at least that would be optional.