I don’t know about FB, but you can use the Twitter API.
GitHub Actions is great for this kind of automation. You could set it up to listen for changes to master directory in the _posts dir and then have a Python script find the last changed file (according to date from filename or git added date etc.) and tweet a link to it.
There are premade Twitter actions in the GH Actions marketplace which can help you with this. Then you could write a shell / Python script which finds the appropriate file and builds the URL, then pass that value to the Action so it tweets a given message.
Or you could write a Python script that identifies the appropriate file and URL and tweets.
I have a template here