I need advice on how to build integration the most correctly

Hello, I would like to implement integration with Monday, for some of our internal applications.
I looked at the integration of the github and noticed that only the webhooks are created on the github, which are sent to https://api-gw.monday.com/automations/github/github-events/xxxxxx
Then the magic happens on monday.
I certainly can use my token to do all the necessary work, but is there no way to make my work more universal (in theory, to integrate with anything), for example, send a web hook and process it somewhere on the Monday side (in my integration app)?
I definitely do not want to use anything third-party, like an integromat.
I just want to understand if I can make Monday integration for my application, as beautiful and convenient as Monday integration and github.
* I took the github just for example.
** The direction of my integration, from my service to manday.
*** My first desire is not to add anything Mondays-specific to the code of my service.