Why do I see rainbows around the moon?
There are a couple of atmospheric phenomena that can create rings around the moon.

Corona are caused by water droplets diffracting the moon's light, they are fairly small, and close to the moon. They are coloured but not as brightly as a rainbow. Our eyes are also not so good at seeing colours in dim light.

The 22-degree halo is a larger ring, as big as two hands stretched out at arms length. Solar halos are clearly coloured, lunar halos are dimmer and I haven't seen lunar halos that are bright enough to appear coloured to me.

An eye condition, astagmatism, can also create rings, such as the "thin blue ring" (though I am not a doctor) You may be seeing a combination of all three at various times.