Semantics, unfortunately matter here. OP did not have a "connection" at MUC. A connection can only occur on the same ticket and OP had separate tickets. Nothing can be done to create a connection where one does not exist.

If OP had been on a single ticket and had misconnected, it would have been UA's obligation to rebook him. But, as his ticket terminated at MUC, UA's duty ended at MUC. Unless his onward carrier agreed to rebook as a good will gesture, OP is stuck with whatever the fare rules are for that ticket.

Terms such as PNR's, bookings, and linking have nothing to do with tickets and connections.

While OP may try to collect against his travel interruption insurance, it is a rare policy which covers across separate tickets.