Does SSE work reliably in mobile browsers nowadays? A few years back when I tried, it was working OK in Chrome for Android but mobile browser support didn't seem complete.
Sadly, there are very few mobile browsers that aren't Chrome or Safari. In fact, Safari/Webkit is the only mobile browser engine available on IOS at all -- all other browsers are just chrome (pun intended) around IOS webkit.
To your point, https://caniuse.com/eventsource
Also there are polyfills for very old browsers like IE.