“Stored messages” should show where a message came from and who you do reply to if you hit the “reply” button.
Actual behavior
In the chat “stored messages” you can not see, where the message came from you forwareded there, so you cannot be sure if you reply to the correct person. Not even the “message details” show that.
That’s because “stored messages” is actually the “message to myself” chat.
We could maybe think about reindroducing the “stared messages” chat, that could have the features you want, but it would be very dificult to implement them into the “saved messages” chat.