The chat never needs an account. This one is only for a payment — a nickname and a password, nothing about you. An account here is not an identity. A nickname and a password — no address, no phone number, nothing that says who you are. It exists only because money does: a subscription has to be cancellable and a balance has to be reachable from your other device. The chat itself needs none of this and never will.
Google sees the sign-in, never your chats. Those stay on our own hardware. Google will know you signed in here, and we receive your email address — nothing else. Your conversations are not affected: they stay on our own hardware and are never sent to Google or to any other AI company.
Not looking for any of this? Use the chat without an account — it is the same chat, and it always will be.