Is stream_socket_server a server for testing, or is it also meant for production?
Is it for making your own Production http (or whatever) server, so you don't need Apache or IIS, etc.?
stream_socket_server is stable if that's what you're wondering. The decision to use it in production to replace existing server solutions such as Apache, Nginx or any other will depend on the quality of tests your run on your solution that uses it.
As with any other project, you start with unit testing, checking if each expected functionality works and look for edge cases, then move it to system testing which implies testing more complete solutions. Once your system tests produce stable results for everyone, you could normally release it in alpha or beta state to encourage user feedback.
After your application has been used by enough people (you decide your thresholds) and there are no more important bug reports open, you can decide to release it in an actual production environment.
That whole process, even in popular applications, can take years. Some applications remain in beta testing for their whole lifetime.
Note that projects such as Nginx and Apache have had centuries (probably millennials) of developer efforts put into them to make them as flexible and stable as they are today.