Sounded like the label for training is the user's action (whether they chose the suggestion provided or not). Then they collect the model updates in bulk from millions of users, that's far more useful for training purposes than a small very well curated data set.

It did mentioned a local version of mini TensorFlow, I would guess the data is cleaned up on local devices and only updates are send back to the cloud.

There is a branch called unsupervised learning, where no labeling is needed.

There is, but supervised and unsupervised learning mostly don't solve the same problems - so this doesn't necessarily help

as I understand what I read the data does leave, but just the users updates - sort of like only your changes to a git a branch are sent when you push.