There needs to be a bit more "group chat" control in Signal messages, wherein you could enforce certain settings for certain chats regardless of the phone settings. You could have group chats that would enforce not showing more information in the notifications, while others would still allow it.
This feels like it would run against the “I bought my device, I should control how it behaves” line of thinking.
The major hole here is that you turn off your notifications and don't have a bunch of database records, but the threat actor somehow finds out who your contacts are, gets a hold of their phone, and can then see all of the messages you sent via their notifications database. So if you want to trust the device for secure communications, you can't do that.