I don't know what the time scale would be, but I think a couple of weeks is probably overly optimistic. Enjoy what you have for now. Could be a year or more for all I know. Somebody may know better. Won't hurt to check, but don't be bothered if it takes a while.
Flushing is an easy DIY thing. See
https://terrylove.com/forums/index....o-flush-a-hot-water-heater.79444/#post-576623 post #7.
I am not saying that this is going to blow out hardness materials. Still, you want to do that on occasion.
If you get a new WH, that could make an instant improvement in your hot. I would not change the WH for that.