That dip tube didn't break off, it may have rotted, much like when your faucet fell off. This was a problem in some tanks in the 90's. When this happened to me I noticed the decrease in hot water and when I checked the lines at shut offs they were blocked with whitish/grey plastic pieces. Didn't know at the time but that was my dip tube, at least what remained of it. I think you would do well to check all hot water lines going to fixtures, dishwashers, shower heads and washing machines, etc. for such blockages. I ran water through the lines for a bit to help flush any remaining pieces. Congrats on the new water heater.