Maybe the kettle has some kind of non-sticking internal surface?

Yes, that sounds like limescale.

Yup. It takes a minute for the scale to build up on the metal.

Kitchens can be very greasy places. Do you ever cook food in a pan near your kettle? It could also be from whatever container you poured the hot water in.

What container is the water in? If it is a mixing cup or glass cup, there will likely be residual fats that linger after washing. There are also various grease,s fats, and other lipids in you water pipes, faucets, and the kitchen air since particles linger around. Everything in a kitchen will start to develop a small film of grease if it isn't cleaned constantly. It's not harmful and you have been consuming it for literally your entire life

Something else I've noticed about my own kettle that might be contributing. I store my kettle very near or sometimes just on my stovetop. If you fry anything nearby, even with a wipe down/cleaning you can still get small amounts of fat splatter on enough of the kettle that some of it may be making it's way into the spout or underside of the lid that then gets mixed in by the steam inside when you boil water next.

Should be, but did someone boil milk at some point?

Do you know if it's a hard water area? It may just be calcium.

When you say "funky", was it a little furry and white? If so, that's probably calcium deposits (aka "limescale").

give it a few days & that ache will mature into a stabbing sensation

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Hava nice day??