You generally need the 16VAC wires from the new transformer to go to the new Video Door Bell. I think most houses install the 16VAC transformer near the circuit breaker box?
If what we see in your picture is a mock-up of what you have in your walls (looks typical), the White & Black wires from the circuit breaker would get cut at the CB panel, and the 120 VAC side would go to the input of the 16VAC transformer.
Then the other half of the cut White & Black lines that go to the doorbell & switch would be connected to the output of the 16 VAC transformer.
Then you would remove the buzzer, tie those two wires together, and that would give you 16VAC on the Black & Purple wires at the new VDB.