Yes. This is the nature of a public square (aka a social platform).
If you need private conversations, use private direct messaging or private group chats (not currently widely available on Nostr clients yet)
Google is like the nosey parker on the street with a camcorder. They ain't doing nothing illegal, but you know that because of this kid, you have to be extra careful what you say out in the open.
There are also some other ideas being explored, like private relays and time-limited messages that relays keep private as best they can, but this is still an open playground with nothing standardised.
Exciting times... because whatever comes from all of this is going to be so much better than Twitter, Facebook, Reddit and sp on.
For now, if you need private comms, use private end to end encrypted messaging.