One of the drawbacks, as I learned - SSE have limit on number of up to ~6 open connections (browser + domain name). This can quickly become a limiting factor when you open the same web page in multiple tabs.
Syncing state across multiple tabs and windows is always a bit tricky. For SSE, I'd probably reach for the BroadcastChannel API. Open the SSE connection in the first tab and have it broadcast events to any other open tab or window.
One of the drawbacks, as I learned - SSE have limit on number of up to ~6 open connections (browser + domain name). This can quickly become a limiting factor when you open the same web page in multiple tabs.