You have to double check with the Classic Center the VIN numbers these parts are meant for. The part number you quoted is the right hand side one for VIN up to ident. no.: 043 002979. Then there was a change with higher 113044 VIN number (044 010365).
Yes, there were different PNs for these parts before (A 110 720 06 04) but they were replaced with those you are looking at.
Good overview is here:
https://www.sl113.org/wiki/ChassisBody/Doors#Latchhttps://www.sls-hh-shop.de/main/en/mercedes-230-280sl-w113-/72-door/72-b-info-door-catchI replaced both (later ones) with parts from Mercedes and they are just fine. No experience with Niemoeller or SLS parts. I see, however, a very similar price - for me it would be clear to go for the original one, but I have only experience with the later one from Mercedes.
I was advised here to really make sure what causes slack in my door latches to replace the correct part. My decision was that it was the bushing inside rubber in the catches got worn out. So I replaced both catches and my life has changed in terms of how the doors close and stay tight.