That's an unusual rust pattern but not impossible. Your wheel has a cloth rim strip? Those hold moisture from rain and road dampness.
There's a chance your rim is not particularly waterproof, so moisture enters through the bead, possibly the spoke holes around the nipples, and maybe even through the tyre carcass. Plus there's sweating/condensation when warm and cool things meet.
Plus black tyres are great at warming up due to sunlight. So warm and wet, plus possible salt can corrode even stainless steel.
Spoke nipples are normally brass which doesn't corrode, but the nickel/chrome coating on the outside makes them look different. Sometimes race bikes have aluminium nipples but these are fragile and oversized and expensive.
You might have plain old chromed steel nipples too, if the wheel is old enough.
Grab some sandpaper and see how deep the rust is - it looks like purely surface rust in your photo.
Fresh nylon rim tape sounds like a good idea, and remove the fabric or paper tape. You don't have to replace the nipples, but they're cheap.