Confused by apparent shorting damage at side and back terminals
Welcome to "why I hate back-stabs and will never use them" 101.

The shorting damage is from arcing between the wire and the poor connection to the back-stab terminal. If it got bad enough, there might indeed have been arcing to the wire continuing to elsewhere. This arcing happens because back stab connections are junk, and don't connect reliably - when they are not connected, the incoming hot wire was 120V while the rest of the outgoing wire and side terminal were 0 volts, until it arced and made a brief connection, possibly even welding itself together for a short period of time until thermal stresses broke the weld and it arced again.

Your circuit breaker would not have tripped (unless it was an AFCI) because the connection was not "directly to ground or neutral" - it was to the loads that were supposed to be solidly connected to the hot, and those loads were either powered (when connected) or not working (when disconnected) but not drawing excessive current in either case.

I honestly have no idea (other than massive skulduggery) how this junk ever got listed. I won't use them, I will remove and replace them if encountered, and I consider them a distinct fire hazard (as you can see.)

Note that not all "back entry wire terminals" are back-stabs - the ones with a plate actuated by a screw are fine (when properly tightened) but the ones where you stick a wire in and do nothing more are utter junk, IMHO. There's a tiny contact area that relies on spring pressure alone to make any sort of contact, and it fails with great regularity.