I'm trying to get more information about what I might be seeing here. I
have a home warranty that will probably get it repaired, but I wanted to
make sure they sent the right guy out (plumber or water heater repairman).

When I'm running hot water in the kitchen, I'm getting a Continual
pounding sound from the water heater. I think it's like water hammer,
but it's at a rate like a woodpecker attacking a tree in a cartoon.

It's happened when running the sink on hot or the dishwasher. Any ideas?