What is the identity of this shiny insulator?

That is common chromate surface treatment. Seen in a great many metal utility items. Not intended to be an "insulator" but perhaps non-conductive as a side-effect.

The red surface of magnet wire is the enamel insulation which is applied as a coating (vs. being an extruded plastic outer sheath as most other wire uses. They use a very thin enamel insulation to get many windings into the space available in a transformer, coil, solenoid, motor, or whatever. It is called "enamel" which it probably was in early days. But in modern times, it is a more sophisticated plastic coating of perhaps several layers. Note that red is only perhaps the most popular color. Magnet wire comes in several other insulator colors also.

Ref: https://en.wikipedia.org/wiki/Chromate_conversion_coating

Ref: https://en.wikipedia.org/wiki/Magnet_wire

Chromating is an anti-corrosion surface treatment for metals. It is not used for insulation. The colour can vary a bit, depending on the process and base metal condition. That's normal.

The layer is greenish-gold in overall color, but have colored patches that may vary from red to green.

Chromate conversion coating. More comonly known as yellow chrome. Wikipedia article

I've tested its resistance with multimeter and it shows infinite ohms

Push harder with your multimeter pins or scratch the yellow surface with a knife first and you will measure short circuit instead though the steel underneath the yellow chrome.