There is no free account. You pay with your data. Recent right to repair legislation in Germany makes the concept of "paying with your data" explicit for the first time even in law text. So courts can no longer doubt that it is paying. But of course it has existed implicitly for years in many contexts. Not sure whether there have been high profile cases whether giving data is "paying" or not. A contract does not require payment by money.

Whether a contract is formed when you register and agree to their terms would depend on locally applicable law. I don't recall stories that courts would have deemed registrations on the internet invalid in general. Certain terms in the aggreement definitely.

The terms of service and privacy policy (https://policies.google.com/privacy) are the contract. And my rough understanding (not based on reading the contract, something said internally at Google a while ago about what is in them) is:

- Your "content" (data in Gmail, Docs, Photos, etc) won't be used for advertising. (Only for personalization, like the Gmail smart compose, asking Assistant about the status of your order, etc.) - Your "activity" (your searches, etc -- what you can see at https://myactivity.google.com/item roughly) can be used for advertising, though you can turn it off (see https://adssettings.google.com) or delete it. (IIUC, you have more granular privacy controls as a logged-in user as you can delete individual items….)