Thank you "Toot Uncommon" for your thoroughness and attention to the problem I am having!
I get the behavior you have described using app switcher. Messages app always appears in app switcher so has not been swapped out. No loss of unsent text. My problem is not with app switching but with screen lock/awake events loosing unsent text. The text is lost only when typed into a "New Message", not when typed in via tapping on an existing conversation.
Here is the result of some tests I have performed that may help diagnose:
1. Tap on an old conversation with recipients A&B. Message history appears. Type the following text: "Test 1". Do not send.
2. Press side button to cause screen lock (or wait for screen to lock automatically).
3. Press Home/TouchID Sensor button to awake.
4. Messages app is still in focus, in conversation with recipients A&B. Unsent "Test 1" is still there. Note: This is normal, expected operation.
5. Go up a level. Select New Message, add recipients A&B. Note: conversation populates with prior messages history, but "Test 1" is missing. Type the following text: "Test 2". Do not send.
6. Repeat steps 2 and 3.
7. The Messges app is in focus, but it is no longer in the conversation with recipients A&B.
Do the following steps in either order, the result is the same:
8. Select conversation with recipients A&B. Message history appears. Unsent "Test 1" is there. Unsent "Test 2" has been lost.
9. Go up a level. Select New Message, add recipients A&B. Conversation populates with prior messages history, but neither "Test 1" or "Test 2" are there. Unsent "Test 2" has been lost.
Conclusion: Unsent text in a New Message is lost through a screen lock/awake cycle.
In case it provides a clue, let me share another observation. When I start a new conversation, as soon as it recognizes the address I have typed in, the window populates with conversation history to that person (if exists). This behavior appears to be different than your statement: "A New Message has no conversation manifestation ...". Furthermore, if I add a second address, it switches and populates window with a different conversation history, one between me and both persons (if exists).