I was in need of server send events as well. Therefore i created this little library: https://github.com/liquidblock/yew-sse
Unfortunately i did not test nor document it (and i did not create an example), but used it like this:

match self.sse.open(
    &url,
    self.link.callback(move |(id, message): (String, String)| {
        Message::SendEventMessage(id, message)
    }),
    self.link.callback(move |value: EventSourceUpdate| {
        match value {
            EventSourceUpdate::Open => Message::SendEventOpen,
            EventSourceUpdate::Error => Message::SendEventError,
        }
    }),
) {
    Ok(task) => {
        self.task = Some(task);
    }
    Err(e) => {
        // error handling
    }
}

self.sse is of type yew_sse::services::sse::EventSourceService and initialized with EventSourceService::new().
self.task is of type Option<yew_sse::services::sse::EventSourceTask> and when dropped it will close the server send event handling.
The onopen, onerror and onmessage events are handled and also the last event ID together with the message is passed to the callback. But i did not implement named events since i did not need them, but was thinking about using a HashMap with the name of the event as a key and the event handler task as a value. With that it would be possible to add and remove named events.
I wrote this library to be used by myself, but also intended to be used with yew and was planning on creating a PR after adding an example, documentation and tests, but never got the time for it.

The library works with stdweb and web-sys, but it was written for yew version 0.16.2.

I'm going to start taking a look at this