Is there a way to use a REST API to grab a list of all deployed applications along with the versions?
We do not have a single API to get all the information you requested.
If you want to know the Applications that are deployed in an environment:
If you know the Application name then the following call be made to know about the current version of the app deployed:
You can find more about the API here: https://docs.xebialabs.com/generated/xl-deploy/10.0.x/rest-api/com.xebialabs.deployit.engine.api.RepositoryService.html