Many of the new beta Microsoft Teams APIs, such as this require the caller to specify the unique ID of the group. Does anyone know how to find a given group's ID?
You can use the joinedTeams API to get all of the Teams that the current user belongs to. The response contains the group ID for each Team.
It looks like you want to use this group ID with the listThreads API. Note that this returns Outlook email conversation threads and not Teams chat threads. Currently, there is no API for reading Teams chat threads - I will update this answer when it arrives.
In the meantime, look at what the Microsoft Graph currently supports for Microsoft Teams. In summary, you can use most of the existing group APIs - for accessing the Team's roster, files, calendar etc. You can also (in Beta) create/read channels and create a new chat thread (you just can't read that thread yet, as above).