The rules for redistributing Newman are clear from its Apache License 2.0 (newman/LICENSE.md at develop · postmanlabs/newman · GitHub). As far as I understand https://www.postman.com/legal/terms/ is the license document for the Postman app. It is not clear to me from the terms whether it is allowed to redistribute the Postman app.
My situation is that I am preparing an artifact for a paper, and I have included a downloaded copy of the free version of the Postman app in the artifact. I use the Postman app in the artifact to allow users to interact with my application which only has a REST interface. The Postman app is only included as means of interacting with my application, the instructions clearly state that Postman is in no way related to my work with a link to the Postman website, and the “Terms of Service” for Postman are included in the artifact. The Postman app is in the artifact as a downloaded copy because the artifact needs to be self-contained and usable even without internet connection, meaning I cant just give a link for people to download Postman from. The artifact will then be archived and publicly available for download by anyone.