Same issue with frigidaire....

It is normal. It is surface rust. Cast iron does that.

Cast iron rusts - period. You should see my Bluestar with the ocean salt air - wow, that's REAL rust. We're talking the old steel igniter screws fusing into the iron burners. I have to drill those things out and re-tap. At least BS learned their lesson and switched to SS screws. And the high moisture in propane does a job on the burners too. But rust is a natural occurrence of varying degrees depending on the conditions - nothing outlandish about your range.

Thanks. Is it safe to assume that the bits that have to function (ignition system, etc.) are positioned in a rust-free area?

And should one season the burner caps? Like one would a frying pan? grease them up and throw them in the oven?

It's normal oxidation. you will see this with all cast iron burners where the surface is raw/unfinished. I wouldn't do more than rub a little thin layer of cooking oil on it and then just leave it alone. It will still look about the same in 10 years as it does now.

"And should one season the burner caps? Like one would a frying pan? grease them up and throw them in the oven?"

I seasoned the grates and bowls on my Bluestar when new three years ago. Since then, the stove top has just become more well seasoned with daily use. I rarely use soap or water on it, and most residue simply wipes off with a paper towel. An occasional burnt on spill might need a bit of soap and water, but not enough to remove the seasoning.

I might add that I live near the beach and salt air, and have no rust on my stove whatsoever.

The oils in well seasoned cast iron will certainly help mitigate rust development.