raccoondad I somehow just read 'With that I mean messages from Messenger apps like Signal, SimpleX not SMS/MMS.', oops.
As for those platforms, its platform/app dependent. However if I am not mistaken Signal stores message data only between the two users in the chat. If you want to make extra sure data is deleted, clear the applications data in the app settings.
There isn't a lot you can do about larger attack entities with physical access, but GOS filesystem-based encryption and the Titan M chip does cover a lot of bases. Regardless an attacker having physical access to a device does harm the security of said device.