It depends on what you’re seeing and how badly damaged the dip tube is, if it’s damaged. A cracked or broken dip tube will definitely cut a hot shower short. But your water heater is fairly young for dip tube troubles, as the tubes typically last 15-20 years.
The only way to find out, though, is to remove the dip tube and carefully inspect it.
As to recircs, they work very well, but they also waste a lot of energy because even with insulated pipes, they are radiating away energy all the time. A better solution might be the Metlund D’Mans, which pulls hot water toward your fixture at the press of a button, and stops when you’re through using hot water.