Hey @RSGDev,
This is a great question! I will do my best to provide some information, but I would also strongly suggest opening up a Feedback request if there is functionality that you would like to see that does not exist today.
In general, an API endpoint does not exist for what you are looking for with all of the information. Below are some suggestions on how to generate a report that you are looking for.
Is it possible to get the install status for a TestFlight user? SORT OF
While the API does not tell you the "Status" of a tester like the console does, if you attempt to send each tester another TestFlight invitation using the below API, you will get a 409 response with the reason why the invitation was not sent. One of these reasons will be: STATE_ERROR.TESTER_INVITE.ALREADY_ACCEPTED. You could use this to determine if a user has at least accepted the invitation and thus has the ability to install the application.
https://developer.apple.com/documentation/appstoreconnectapi/send_an_invitation_to_a_beta_tester
Is it possible to find out which "Version" of an application a user has installed? NOT THAT I KNOW OF
Not sure if this would be helpful, but I have a tool that goes through and generates a report on every application in our App Store Connect account and which builds each tester has access to and dumps that out to a CSV file. The way that I do this is through the below steps.
Capture the App ID (https://developer.apple.com/documentation/appstoreconnectapi/list_apps)
Request ALL TestFlight Beta Groups (https://developer.apple.com/documentation/appstoreconnectapi/list_beta_groups)
Request ALL TestFlight Beta Testers for each Beta Group (https://developer.apple.com/documentation/appstoreconnectapi/list_all_beta_testers_in_a_beta_group)
Attempt to resend ALL TestFlight Beta Testers an invitation to the application (https://developer.apple.com/documentation/appstoreconnectapi/send_an_invitation_to_a_beta_tester)
The above steps will give you all of the information that you need in order to generate a table with each tester, the builds they have access to along with whether or not they have accepted the invitation and are attempting to use the application.
One major note on the above steps. If you are not dealing with thousands of testers, I would not worry about this, but once you are testing with thousands of users, I would strongly suggest sorting by user email and NOT by the tester ID. I actually include that as a part of my results due to the App Store Connect API creating multiple "users" for the same email.
I know this doesn't answer the direct question you are looking for information on but hopefully this helps and make sure to fill out a Feedback so Apple can help provide what you are looking for!