Not that I necessarily think it's best to stay with Postman, but have you looked at newman, which is the CLI runner for postman configs? We had postman as a test suite for something (which is more an API than an app), and I got tired of having to deal with setting up extra steps to test and of exporting the postman config to save in the repo, so I put newman on the test system and just run against the config directly in the test environment and check the output.
I don't necessarily recommend editing the postman config json directly to set up new tests as it's a PITA, but it's generally what I do so I don't need to keep importing and exporting it with Postman.
A tool designed for working with on the shell is likely better than what I'm doing with newman (since the config is not the most accessible), but it also meant I didn't need to rewrite a bunch of existing tests and verify they actually did the same thing.
The problem Newman/postman have is the same for every GUI based testing application. They almost always produce non human readable config files. Making any kind of code review of such changes at best extremely painful and at worst impossible.
IMO any testing tool that does not save it's test classes in a human readable format is DoA.
I don't necessarily recommend editing the postman config json directly to set up new tests as it's a PITA, but it's generally what I do so I don't need to keep importing and exporting it with Postman.
A tool designed for working with on the shell is likely better than what I'm doing with newman (since the config is not the most accessible), but it also meant I didn't need to rewrite a bunch of existing tests and verify they actually did the same thing.