HomeAI is a private system run by one household for its own use. This page says what it does with the Google account data it is given access to.
Only members of the household that runs it. Each person connects their own Google account, and can withdraw that access at any time from their Google account's security settings.
The email in the connected Gmail account: messages, their labels, and details such as sender, subject and date.
It reads the mail in order to sort it into categories, and adds or changes category labels on messages. It does not send, delete or move mail.
On a computer in the household's own home. Email is categorised by software running on that computer. The household may also use outside tools to maintain the system.
No one. The data is not sold, shared, or used for advertising, and it is not used to train any general-purpose AI model.
HomeAI's use of information received from Google APIs adheres to the Google API Services User Data Policy, including the Limited Use requirements.
A household member can ask for the stored copy of their mail to be removed, and can disconnect their account, at any time.