So far I only used HTTP/1.1, but recently I switched to HTTP/2. On 1.1 I ran into request number limit issues, but HTTP/2 uses one connection with multiplexing, does that mean that I can keep multiple SSE channels open with no problems, or should I still use only one with some internal message routing solution?
If you want to be safe: Use just one channel or only a few of them and multiplex internally.
Longer answer: The reason that more channels caused problems with HTTP/1.1 is that each channel required a dedicated TCP connection, and browsers limited the number of concurrent TCP connections for each tab (I think to something around 10). With HTTP/2 making concurrent HTTP requests is possible on a single connection. therefore opening multiple concurrent SSE streams is more likely be possible. However browsers (and also webservers) may still limit the number of concurrent HTTP/2 streams they support over a TCP connection. HTTP/2 even supports that by allowing each peer in a HTTP/2 setting to communicate the maximum amount of concurrent streams it supports (SETTINGS_MAX_CONCURRENT_STREAMS). To be safe you would need to figure out what the limit is that your target browsers and your web server supports and use a lower number of SSE streams. I unfortunately don't know whether it's part of any HTML or browser specification, that they all should support at least a well-specified number of concurrent requests over HTTP/2. If you keep the number of requests low you avoid to run into problems.
One other advantage for using only a few channels is that you can still support HTTP/1.1 clients well. And not only those which might be directly connected to your server but also those which might connect through a proxy-server (which means the connection browser<->proxy uses HTTP/1.1 and proxy<->webserver uses HTTP/2).