On primal, if I don't follow them, their DMs are on a separate tab which I would not check all the time. That's also how the big social media platforms do it. I found a guy's bag and tried to contact him on Facebook and Instagram. He hasn't seen my DM for weeks now as these DM's don't get shoved in his face as they shouldn't.

On nostr we could bribe the recipient into reading our messages but otherwise, unsolicited messages - from ephemeral accounts even - should never cause some inbox notification.