If the site is hardcore SPA, and has a single "mysite.com/" URL, then you're right that state is only represented in terms of websocket events. However, if we have URLs like "mysite.com/users/alice" or "mysite.com/conversations/alice-bob-23", those resources will stay current, so that reloading them will reflect websocket events that took place since the last load. If the events are coming really quickly, there might be a race condition, but that's easy enough to solve by including a "last event" token in the page itself, that can be included in the websocket URL.
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If the site is hardcore SPA, and has a single "mysite.com/" URL, then you're right that state is only represented in terms of websocket events. However, if we have URLs like "mysite.com/users/alice" or "mysite.com/conversations/alice-bob-23", those resources will stay current, so that reloading them will reflect websocket events that took place since the last load. If the events are coming really quickly, there might be a race condition, but that's easy enough to solve by including a "last event" token in the page itself, that can be included in the websocket URL.