I know SMA tab got replaced with Admin studio, but in SMA we can see the config changes like Administration section and click Configuration Management to display the configuration settings for the prconfig.xml file
Using Pega API is extremely easy. If this is your own local environment where you do not have to worry about security, just turn off 'use TLS/SSL' and 'requires authentication' for the service package 'api' (see the screenshot) below:
Then click 'Try it out' button. In your case, use nodes endpoint to get the nodeid and then pass that to the required parameter for the download prconfig endpoint.
You can of course use your own REST client, e.g., soapUI, postman (all free tools).
Now if this is your company env, your system admin should have secured the pega API and provided you the credentials to access any endpoint, whether that is OAuth2 or Basic Authentication etc.
Providing Restful endpoints has been the prevailing industry standard for a while now and will continue to be the investment area for many software vendors. It has great advantages over the old SMA, e.g., no extra deployment of SMA (which has been proven to be maintenance headache for system admins); allowing client to build their own UIs (even outside Pega) and perfect fit for the future-facing microservice based cloud native architecture.
Hope this helps! Enjoy the journey! It is common that you feel bit confused and you are not alone - this is true for any new stuff.