Move process package integration tests to own files
What does this MR do?
It segregates the integration tests from the process package into _integration_test.go files (so it can be easily tagged later).
Why was this MR needed?
Integration tests are currently mingled with unit tests, making it difficult to know where to add a new integration test, or for example to run only unit tests ignoring integration tests.
What's the best way to test this MR?
Check that moved tests still execute in the CI job.