When Veeam first announced the support of backup of Teams Chats via the Graph API, there was some general confusion that this was adding new capabilities to Veeam Backup for Microsoft 365.
The graph API that is mentioned refers to a change coming to the way Microsoft allows Veeam to access Teams data. Microsoft says it will be deprecating the old way Teams data is accessed by Veeam but is not an immediate change for all customers. When this change is rolled out to your Microsoft 365 organization, a configuration change will be required on both your Microsoft 365 Organization and Veeam Backup for Microsoft 365. Switching to the graph API is something that can be done today, but it does incur more charges from Microsoft.
Veeam still does not support backing up Chat data for one-to-one, or group messages so the data in this section of the Teams app cannot be backed up:
The “chats” that can be backed up by Veeam are “posts” or “conversations” within a Team as shown below:
Here is the documentation from Veeam when you are ready to switch over to the Graph API Access, or when Microsoft deprecates the old “EWS APIs” access.