How long did you let the server run? It seems that it is still starting because of the high CPU usage, the first start from RUST can take very, very, very long (I think mine took about 10 minutes and remember this was after the download from the game finished).
After the container or better speaking the server started something like that should show up (keep in mind I didn't forward the ports to the outside world, that's why you see the last message):
As you can see the server shows up in the Steam Server browser just fine (even not forwarding the ports to the outside world) if you are adding it with YOURSERVERIP:28016
As for the CPU usage and has nothing to do with the container this it the dedicated RUST server, however that is pretty normal IIRC for RUST, on my i5-10600 it utilizes in idle almost 8% CPU.