The voltage dropped after you started the car or before? If it drops after you start it then it's not so bad. 11.9 under load is pretty good which is the best indication of battery health. If you have a bad cell you will get decent power for a while but then a precipitous drop in voltage as the weak cell runs out of juice and is dragged along by the other cells.
The battery should recover somewhat with use. That's a pretty good charger so that's not your problem. It's probably a little hard sulfated from sitting around. I'm not convinced the desulfation works but I do it anyway because it can't hurt. there is a powder which removes the hard sulfation but this reduces the potential capacity of the battery so It's only a last resort after trying desulf and exercise.
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