If you wanted to run a Postman collection, you could use Shell.ShellExecute to invoke Newman CLI.
If you are trying to invoke Postman API to manipulate a workspace then take a look at WebRequest.
The rules say “Entrants must create a public Postman workspace that is useful, has business value, and engages the community. Projects must have at least one (1) collection.”
My take on this hackathon (which could be wrong) is that we should focus our energy on making our public workspace awesome and something that people will end up bookmarking and using. I think your entry and the judging is focused on the public workspace, so I’m not sure that building the app around your workspace will count toward the contest? or Maybe it does?
Hopefully one of the judges can comment on that?