PTE or Permanent Test Environment also referred to as Staging environments. The purpose is to be as close to Production environment as possible. So running in the same type of container in the same datacenters with a shared load across both datacenters with access to the same services Production would have access to. The goal with local development is to be as close to Production as possible but running the service locally instead of in the datacenter. So the number of differences between local development and Production is small. The number of differences between Staging and Production is even smaller(basically only size of data and users).

To add an extension to a PTE envronment would be a deploy exactly like a Production deploy. The only difference being that we have a little less process around deploying to Staging as it isn't mission critical that Staging has as much uptime as possible. To learn how to deploy something see the documentation here:
https://docs.q2developer.com/guides/processes/review_and_deploy.html

To actually test in that environment, for FIs someone at your institution has credentials to Staging. If not, you can reach out to your CSM. For Partner Marketplace and Partner Accelerator, we provide those credentials during the App Review process.