The REST API you probably are looking for is the OSLC API, which is formally specified and supported. Below I added a link to a workshop document and resources for that API, and that should get you going, as it explains things like authentication (browser and Postman requests work as you are already authenticated through your browser) and how to navigate the data available in the application.
Note that Java is used in that workshop, but you should be able to translate that fairly easily to C#.

For completeness, the DNG public API's that are available are:

• RRC Reportable API - creating custom reports to be run from DNG or RPE, read only.
  

• OSLC RM V2 API - the open standard way to programmatically integrate with DOORS Next Generation, there is an elaborate workshop to get you started here OSLC Workshop article. These programs can be from any language that support HTTP REST calls, e.g. Java, C# etc. Hence these are more flexible to run and can read and update DNG data, as part of a web server, or standalone, but have some limitations set by the current OSLC standard, for example module support.
  

• TRS 2.0 - the OSLC Tracked Resource Set open standard REST API to hook into the stream of low level changes done to resources in the DNG application (and other Jazz apps as well); read only.

• and additionally, there is the so called client extension capability, these are Javascript extension that generally added as widgets you can run from the dashboard, and can be used to view and edit DNG data. It's more tailored to DNG, so has better module support, but is limited to run in a browser/javascript environment.