It's federated AI. Part of the AI runs locally and part on their servers. More importantly, the part that runs locally is sent to the server from time to time to update their global model. Just the weights are sent. So, in theory no personal information leaks but Google gets the AI that everyone helps train 24/7.
Discussion
I also suspect this, but I use it without the network permission*, so only the local AI is active, and I don't see any problem.
Having billions of users training the AI 24/7 is a huge resource, but the quality improvement should be marginal at this point since the current quality is already very good; I'm surprised that someone else cannot emulate it, even if with less data.
* I keep the permission enabled only few minutes after the installation to download the additional languages and any possible update.
All you need is the local AI from time to time. Reinforced learning is subtle but very important to keep an edge on everyone else.