The rainbow stains are caused by chromium in the steel reacting with oxygen in the air to form an extremely thin layer of oxide on the surface. The thickness of that layer is stupidly thin (on the order of the wavelengths of white light). That layer refracts different wavelengths at different angles and causes the rainbow hues.
For all intents and purposes, the rainbow stains don't exist (other than visually). They won't interact with food, they don't change taste or smell—they effectively are not there. (The patina you see on carbon steel knives is much the same thing, a microscopic layer of oxide.)
Cook something else in the same pan, and the coloration may change, or disappear, or appear in different areas. It depends on the food, how much acid and salt is in it, how hot the pan gets, the phase of the moon, and whether a butterfly flapped its wings at the right moment on another continent…