Your door bell has 4 x 1.5 volt batteries = 6 volt, Nest uses 16 to 24 volt, common in USA but not in UK, so to use Nest in the UK it seems one needs a relay so a 6 volt bell will work on a 24 volt nest.
In your Nest picture the door bell terminals 1 and 2 just connect the wires together, 0F and 3T actually work the door bell. It seems reading the internet instructions people connect a 24 volt relay where it shows 0F and 3T then the relay works the door bell.
When Hive and Nest heating controls first came to UK we had problems, then they released a UK version, I suspect same will happen with their door bell, in time they will likely market a version that has the twin voltage transformer and relay built in.