How to write an application for monitoring connections on a remote server?

Question

Monitoring

In general, I have over several hundred servers in my work for relaying data to a central server via a satellite connection via a proxy via checkpoint. Quite often, various kinds of problems arise on servers, and one of them is the loss of connection with objects from which data is relayed. I would like to automate the detection of this problem and save myself from routine work, at the moment I need to log in via RDP on a narrow channel.
As I understand it, I need to write a server and an application client so that they can work through port 443.
What to write on? What framework to use? Maybe there are more tips?
Perhaps I didn’t put it quite correctly, since my development experience is a couple of android games and an extension for a CAD system. I am fluent in java and lua.
Ready-made programs are not interested, I want my bike.