Short answer in general: NO.
You can't create another factorio client without reverse-engineering the current one as the source was not licensed to you in a legal manner.
At best you shall be in a gray zone then. There is at least 5 server scanners and 4 ddos modules that I recall meeting in the wild so you should rather not go this way if possible. At worst you shall be violating a certain act and possibly also your local laws. Not quite worth the trouble.
There was/is a clusterio mod that is a server-to-server communications basically. You can get the idea of what is possible by youtubing some of it. And it's a lot.
There is an rcon interface (see source rcon) which is basically a [`] key console from a possibly remote or tunneled location; allows for running commands for example. But shall require some heavy groundwork.
There is a chat-sync for discord bots. They act differently but all you want to know -- the server runs a mod or a scenario module. Then there's an agent of that bot running at server which in turn communicates somehow with the one outside. Be it rcon or local files or whatever.
You need to control the server.
If by scoreboard you mean the one that is of RedMew scenarios or Comfy Scenarios then its more then possible -- it is ready and running. Comfy' one even shows you the birdview over the person you hoover over at scoreboard for example.
If you want to dump that then you can use smth like serpent.line(data) or smth alike
If you want to make the rcon reciever from the ground up (for some strange reason)
for rcon specs you can see this;
https://developer.valvesoftware.com/wik ... ol#Node.js
for how-to-make-a-loopback-server-with-node use google then gear it together. 2h is more then enough probably.
Then just set localhost:someport as rcon interface in factorio config (or the-rest settings) and get up ssh with a tunnel option (or any other tcp tunnel) if necessary so you would get the rcon from where you want it. Just remember rcon is too raw and bulk for anything big so some checks and validations are necessary if you come this way.
B: script output
just dump to file as most lua scripts do. It shall be in the game dict so you can set a hook or smth of your liking; then you xz or lz it and then you tar it with other stuff you want to send (or the other way around) and use that old scp (ssh file transfer) or sftp with filezilla or even a simple node light-server to serve a dir or a python web server or even apache/nginx/proxy/socksy/woxy/cgi/php etc and etc. That way you can even get stats from a bunch of sharehosted servers in a tar.