The main benefit of HTTP/2 for SSE is having just one server connection regardless of how many naively implemented widgets you have on a single page. SSE works

The main benefit of HTTP/2 for SSE is having just one server connection regardless of how many naively implemented widgets you have on a single page. SSE works just fine over HTTP, but it does keep a socket open to the server per each connection, so a badly architected client can exhaust server resources quite fast