Dear @sjosey, thank you for your warm welcome.
Thank you for pointing me towards the V1Transactions API - it seems to be exactly what I need.
Just to explain the source of my confusion: I can see now that on v1-transactions.md it does not say that it is deprecated, as the other V1 APIs do. However, on the main readme.md file (GitHub - square/square-java-sdk: Java client library for the Square API), the V1 Transactions API is listed under the “Deprecated APIs” heading. Perhaps this needs to be revised for the sake of clarity?
Also, one side question which I don’t think was answered: Is there an API to query the current balance of your Square account? I would like this as a cross-check during automatic reconciliation to make sure that the actual balance (as reported by Square) matches the balance we expect according to our our own internal reconciliation. Or is the idea that entire balance transferred at each settlement, and so we can infer the Square Balance by looking at the settlement amount?