Has anyone come across a good semi-technical description of "how your node knows that its message got sent and reached its destination and can stop sending"? I'm interested in how this logic is executed when you can't be sure (I assume) that knowledge of the result will get back to you in a certain amount of time.

You can find that here in the Layer 2 section: https://meshtastic.org/docs/overview/mesh-algo/

In short, all messages are sent within windows, which include waiting periods within which the broadcasting node listens for any other node to rebroadcast the same message. Upon seeing the message be rebroadcast, it stops attempting to send.