Why is the “process” field empty for you? That’s the most interesting field.
Personally I had to add a -p to ss to see the process (maybe have a different version of ss or something).
For me it looks like this
$ ss -tulwnp | grep 5600
tcp LISTEN 0 128 127.0.0.1:5600 0.0.0.0:* users:(("aw-server",pid=9725,fd=6))
As you can see, owned by aw-server.
I have no idea what esmmanager is, should not be related to activitywatch.
Changing the port is not risky, but then you also have to change the port for all the clients (easy for aw-watcher-window and aw-watcher-afk, but for some watchers like aw-watcher-web you need to build them manually from source).