I have the same noise. I changed out the check valve. It is a cheap valve with a plastic plunger & spring. New one cost 6 bucks at CW.
The one I removed looked ok. But I replaced it. Same noise.
I now replaced it with a manual valve to hand shut off the water to do the winterization. The noise is still there although not as bad.
I have flushed the tank several times through the plug / anode hole by sticking a hose in, and flushed the tank running water through the back with the plug / anode hole open.
The tank is in an 09 fiver and the noise was not there for a couple / 3 years, then it just started. I took out the existing check valve with a break bar and 1 1/8 or 1 1/16 deep socket. Can't remember what size socket for sure. It was hard to get to and I had to remove some of the duct work for the furnace to get to it. Then hold the tank down with one hand and the break bar in the other. It will come out but is in there tight.
I used the brass check valve as a small nipple to connect up my manual
valve. I just broke out the inside plastic plunger & spring. The inside of the brass fitting is somewhat of a reducer to get the plunger to work. My thought now is maybe by using it as a nipple with the reducer effect it is changing the water flow somewhat and making the noise. As I said before, its hard to get at and I have some what learned to live with the noise. Good luck with what ever you decide.