Install NWJS, it's node with an embedded browser app:
https://nwjs.io/
Download, install, copy and paste your javascript code into the index file, save it and go launch the NWJS app... and you're pretty much done setting up your local node server.
Edit: I just noticed you want to be able to send the request the other way around, right?
So, http request goes from your public website server -> to your client PC at home, which will return it back to the webserver and serves it to the visitor? Your public website would become a reversed proxy pointing to your local machine...
You would probably need a static IP address and open up a port in your router, if you want to have your VPS or webserver make a direct connection with your PC at home, as you would either need to open up a port to expose your local HTTP server at home. You probably want this for the webhook to return the status of the payment, I assume?
Wouldn't it be easier to just run a tiny script on your local pc, that simply sends the latest "data" every 30 seconds or whatever, to a public url on your hosting/VPS? Basically a cron job.
If you do need a quick and dirty way to expose a port on your local machine, LocalXpose is a working and out of the box solution by allowing you to route it through their servers to your home PC.
Easy, one click setup basically:
https://localxpose.io/