That settings menu gives you two relevant options:

1. The ability to delete specific conversations,

2. The ability to not use "conversation memory" at all.

It doesn't provide the ability to forget specific details that might be spread over multiple conversations, including details it will explicitly not tell you about, while still remembering. That's the point -- not that it's using summaries of user conversations for memory purposes (which is explicitly communicated), but that if you tell it "Forget about <X>", it will feign compliance, without actually removing that data. Your only "real" options are all-or-nothing: have no memories at all, or have all your conversations collated into an opaque `user_context` which you have no insight or control over.

That's the weird part. Obviously, Google is storing copies of all conversations (unless you disable history altogether). That's expected. What I don't expect is this strange inclusion of "prohibited" or "deleted" data within the system prompt of every new conversation.